The generator matrix

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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+78x^72+126x^73+267x^74+350x^75+597x^76+630x^77+719x^78+956x^79+1081x^80+1106x^81+1265x^82+1470x^83+1533x^84+1688x^85+1737x^86+1756x^87+1787x^88+1934x^89+1742x^90+1774x^91+1617x^92+1522x^93+1352x^94+1234x^95+1048x^96+852x^97+698x^98+478x^99+427x^100+264x^101+243x^102+140x^103+127x^104+60x^105+35x^106+24x^107+18x^108+8x^109+3x^110+10x^111+6x^112+2x^113+1x^114+2x^118

The gray image is a linear code over GF(2) with n=176, k=15 and d=72.
This code was found by Heurico 1.11 in 77.6 seconds.