The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+92x^77+414x^78+846x^79+1490x^80+2280x^81+3130x^82+3982x^83+5024x^84+6416x^85+7673x^86+8476x^87+9573x^88+10260x^89+10832x^90+10968x^91+9756x^92+8966x^93+7742x^94+6406x^95+5189x^96+3906x^97+2842x^98+1938x^99+1232x^100+646x^101+409x^102+252x^103+161x^104+74x^105+44x^106+24x^107+20x^108+2x^110+4x^111+2x^112

The gray image is a linear code over GF(2) with n=360, k=17 and d=154.
This code was found by Heurico 1.13 in 294 seconds.