The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+346x^79+651x^80+1050x^81+1762x^82+2316x^83+2634x^84+3400x^85+3769x^86+4494x^87+4485x^88+5276x^89+5095x^90+5232x^91+4694x^92+4758x^93+3814x^94+3496x^95+2617x^96+1964x^97+1374x^98+972x^99+603x^100+348x^101+173x^102+100x^103+52x^104+34x^105+13x^106+4x^107+4x^108+2x^109+2x^112+1x^140

The gray image is a linear code over GF(2) with n=360, k=16 and d=158.
This code was found by Heurico 1.13 in 76 seconds.