The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+40x^78+68x^79+178x^80+224x^81+408x^82+528x^83+691x^84+892x^85+963x^86+1018x^87+1143x^88+1370x^89+1302x^90+1382x^91+1320x^92+1102x^93+1003x^94+852x^95+560x^96+410x^97+292x^98+216x^99+162x^100+84x^101+58x^102+30x^103+25x^104+10x^105+18x^106+2x^107+9x^108+2x^109+7x^110+5x^112+2x^113+4x^114+1x^116+1x^118+1x^124

The gray image is a linear code over GF(2) with n=360, k=14 and d=156.
This code was found by Heurico 1.16 in 23 seconds.