The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  X  1  1  0  X  1  0  1  1  1  1  1  1 X^2  X  1  X  X  1  1  X  1  X X^2 X^2  1  1  X  1  X  1  1  X  1  1  1  X  1  0  1 X^2  1 X^2  X  X  1 X^2  1  1
 0  X  0  0  0  0  0  0 X^2  X X^2+X X^2+X  X  X X^2+X X^2+X X^2 X^2  0  X  X X^2+X  X  0  X  X  0 X^2+X  X X^2 X^2 X^2 X^2+X X^2+X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X X^2+X  X  0  X X^2+X X^2  0 X^2  X  0 X^2+X  X  X X^2  X  X  0 X^2 X^2+X  X  0 X^2 X^2+X  X  0 X^2+X  0  X  X  X  0 X^2+X X^2  X  0 X^2 X^2+X X^2+X X^2  0  X  X  X  X  0  0  X  0  0
 0  0  X  0  0  0  X X^2+X X^2+X  X  X X^2  X  X X^2  0 X^2 X^2+X X^2+X X^2+X  0  X X^2+X X^2+X  0 X^2+X X^2+X X^2 X^2  0  0 X^2 X^2 X^2+X  0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X  0 X^2+X  X  0  0 X^2 X^2  X  0  X  0 X^2+X  X X^2 X^2  X X^2 X^2 X^2+X X^2+X X^2+X X^2 X^2+X  0  X  0 X^2 X^2+X X^2 X^2+X X^2+X  X X^2+X  X X^2+X  X  X X^2  X X^2 X^2  X  0 X^2  0  0  0 X^2+X  0
 0  0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X  X X^2 X^2  0  0  0 X^2 X^2 X^2+X  X X^2+X  X  X  0  X X^2 X^2+X X^2+X X^2+X  X X^2+X X^2+X X^2+X  X  X  0 X^2 X^2 X^2+X X^2  0  X X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X  0  X  0  0  0  X  0 X^2 X^2  0 X^2+X X^2 X^2 X^2+X X^2  X X^2+X  X  0 X^2+X X^2 X^2+X X^2+X X^2+X  X X^2+X  0  0  X  0 X^2  0  0 X^2+X  0 X^2  0
 0  0  0  0  X  X X^2 X^2+X  X X^2  X  0  X  0  X  X X^2+X X^2+X  0 X^2  X  X X^2  0 X^2 X^2+X X^2+X  0  X  0 X^2  X X^2+X  X X^2+X X^2 X^2+X X^2  0  0  X X^2 X^2 X^2 X^2 X^2+X X^2  X  X  0  X  X X^2+X  X X^2+X  X X^2+X  X  X  X X^2+X  0 X^2+X X^2+X X^2 X^2  X X^2+X  0  0 X^2 X^2  0 X^2+X X^2  0  0  0 X^2 X^2  0  0  0  0  X X^2+X  X X^2+X  X  0
 0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0  0  0

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+17x^80+82x^81+116x^82+190x^83+219x^84+208x^85+216x^86+326x^87+317x^88+290x^89+382x^90+266x^91+283x^92+272x^93+196x^94+138x^95+119x^96+108x^97+70x^98+78x^99+47x^100+50x^101+38x^102+20x^103+18x^104+10x^105+2x^106+6x^107+2x^108+2x^109+2x^110+2x^113+2x^114+1x^132

The gray image is a linear code over GF(2) with n=360, k=12 and d=160.
This code was found by Heurico 1.16 in 2.22 seconds.