The generator matrix

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

generates a code of length 90 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+56x^72+80x^73+313x^74+346x^75+585x^76+744x^77+1038x^78+1148x^79+1456x^80+1670x^81+1958x^82+2142x^83+2529x^84+2916x^85+3048x^86+3362x^87+3414x^88+3842x^89+3752x^90+3914x^91+3534x^92+3470x^93+3211x^94+3104x^95+2667x^96+2384x^97+1997x^98+1584x^99+1397x^100+958x^101+861x^102+606x^103+474x^104+270x^105+273x^106+156x^107+119x^108+38x^109+48x^110+20x^111+20x^112+10x^113+11x^114+2x^115+4x^116+2x^117+1x^118+1x^126

The gray image is a linear code over GF(2) with n=180, k=16 and d=72.
This code was found by Heurico 1.11 in 356 seconds.