The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 0 1 1 0 1 0 1 X X X 1 X 1 1 0 1 X 1 1 1 X 1 0 0 0 X X 1 1 0 X X X 1 0 0 1 0 1 1 1 X X X X 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 X X X 1 1 0 X 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 X+1 1 1 1 1 X+1 1 1 1 X+1 0 X+1 X+1 1 X+1 0 0 1 1 1 X X 1 X X 1 1 0 1 1 1 1 1 1 1 0 0 X X X X 1 1 0 1 1 X 1 X+1 0 1 X X+1 0 0 1 X 0 X X+1 1 1 X 1 X 1 X X 1 0
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 X X X X 0 X X X 0 X 0 X 1 1 1 1 1 X+1 1 X+1 1 1 1 X+1 1 X+1 0 X+1 1 X+1 X+1 1 X+1 1 0 1 1 X X+1 1 1 0 X 1 X 0 X+1 1 X X+1 1 X 0 0 1 X+1 X+1 X+1 X X X 1 X+1 0 X X X+1
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 1 X X+1 1 0 X X+1 X X X+1 X+1 1 0 0 1 1 1 0 1 X 0 1 X X+1 1 1 X+1 1 X+1 0 X X+1 1 X+1 X X+1 X+1 1 0 0 X X 0 0 X 0 X+1 X+1 1 X 0 1 1 0 0 0 X+1 0 0 1 X+1 X 0 1 0 X+1 0 X X X+1 0
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 1 X 1 X+1 0 0 X 1 1 X 0 X+1 1 X+1 X X+1 0 X+1 X X+1 X 1 1 1 X 1 0 X+1 X+1 0 1 1 X 1 1 0 X+1 X X 0 X 1 0 1 0 0 0 X+1 X+1 0 X X X+1 X+1 0 1 0 X+1 X+1 1 X X+1 X X+1 0 X X+1 1 0 X+1 1
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X X+1 1 1 0 1 X+1 X 1 X+1 X X X 1 0 X X+1 X X+1 X 1 X 0 0 X 1 0 1 1 0 0 X+1 X+1 X X+1 0 1 X 1 0 1 0 X X 1 X+1 1 X+1 X+1 0 0 0 X+1 1 X X 0 X+1 X+1 X X 1 X 0 1 0 X+1 0 1 X+1 0
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 0 0 0 X+1 1 1 1 1 X 0 X X+1 0 1 1 X+1 X 0 X 1 0 1 X+1 1 1 1 0 1 X X+1 X+1 0 1 X 1 X X X+1 1 0 0 X+1 0 X+1 0 1 0 X+1 X+1 X 1 X+1 X+1 X+1 1 X 1 X+1 0 X 0 X+1 0 X 1 1 X+1 0 0 X+1 X+1

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+88x^74+142x^75+279x^76+358x^77+403x^78+514x^79+558x^80+688x^81+749x^82+708x^83+750x^84+868x^85+865x^86+848x^87+883x^88+874x^89+833x^90+828x^91+806x^92+750x^93+674x^94+634x^95+534x^96+438x^97+348x^98+288x^99+224x^100+166x^101+118x^102+60x^103+52x^104+16x^105+18x^106+10x^107+8x^108+2x^109+1x^132

The gray image is a linear code over GF(2) with n=176, k=14 and d=74.
This code was found by Heurico 1.10 in 16.7 seconds.