The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+113x^72+188x^73+370x^74+496x^75+747x^76+926x^77+1265x^78+1418x^79+1636x^80+2062x^81+2248x^82+2630x^83+2789x^84+3132x^85+3485x^86+3502x^87+3649x^88+3860x^89+3628x^90+3680x^91+3473x^92+3196x^93+2995x^94+2802x^95+2470x^96+1992x^97+1724x^98+1374x^99+1043x^100+804x^101+611x^102+418x^103+295x^104+184x^105+174x^106+60x^107+36x^108+38x^109+12x^110+4x^111+3x^112+2x^113+1x^152

The gray image is a linear code over GF(2) with n=178, k=16 and d=72.
This code was found by Heurico 1.11 in 359 seconds.