The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 X 1 1 X 0 1 1 1 X 1 1 0 1 1 1 1 1 X X 1 X 1 1 1 1 1 X 0 1 1 1 X 1 1 X 1 0 1 0 1 1 0 1 0 X 1 1 1 1 X 1 1 0 0 0 1 1 X 0
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 1 0 1 X 1 X X+1 0 1 X+1 X 1 X 0 X+1 0 X 1 X 0 1 X X+1 1 X+1 1 0 0 1 X 1 1 1 1 1 X+1 0 1 1 X X 1 0 1 1 X 0 X+1 1 0 X X+1 X 1 1 X+1 0 0 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 1 1 X X X+1 X+1 X+1 0 X X+1 X 1 X 1 1 X+1 1 X 0 1 X 1 X 0 1 1 1 X X 1 X+1 0 X 0 X X+1 X+1 X 0 0 X+1 0 X+1 1 0 X X 1 X X+1 0 1 1 X+1 0 0 X
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 0 1 1 X 1 0 1 X+1 0 0 1 0 X+1 0 1 X X+1 1 1 0 X X+1 X X 1 1 1 1 0 1 X+1 1 X+1 0 X+1 1 X 1 1 X+1 1 X+1 X 0 X X X+1 0 X+1 1 X X 1 X 1 X+1 1 1 1
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 1 X+1 0 X+1 0 X+1 X X+1 X 1 X 0 X X 1 X+1 0 1 X X X+1 X X 0 X X 0 X 0 0 X 1 X 0 X+1 X+1 1 1 X X X+1 X 0 X X X+1 X X+1 0 X 1 1 1 1 X 1 0 0 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X 0 0 0 X X 0 X X X 0 0 X 0 0 X X 0 0 0 X 0 0 X 0 0 X 0 X 0 X X 0 X X X X 0 X 0 0 X 0 X X 0 0 X 0 X 0 0 0 0 0 0 0 X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X 0 X 0 X X 0 0 0 X 0 0 X 0 0 X X X X 0 X X 0 0 X 0 X X 0 0 0 0 0 0 X X 0 X 0 0 X X 0 X X X 0 X 0 X X X X 0 0 X 0 0 X X
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X X X X X 0 X X X X X 0 X 0 X 0 X 0 X 0 X X 0 X 0 X 0 X X 0 0
generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+147x^72+482x^74+715x^76+702x^78+819x^80+886x^82+913x^84+804x^86+807x^88+644x^90+555x^92+348x^94+195x^96+92x^98+57x^100+10x^102+14x^104+1x^112
The gray image is a linear code over GF(2) with n=168, k=13 and d=72.
This code was found by Heurico 1.16 in 14 seconds.