The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+384x^77+768x^78+1358x^79+2073x^80+3204x^81+3771x^82+5570x^83+5862x^84+8370x^85+8206x^86+10126x^87+9915x^88+11144x^89+9984x^90+10822x^91+8475x^92+8608x^93+6163x^94+5362x^95+3713x^96+2866x^97+1652x^98+1242x^99+587x^100+396x^101+141x^102+138x^103+86x^104+34x^105+29x^106+6x^107+8x^108+2x^109+6x^110

The gray image is a linear code over GF(2) with n=356, k=17 and d=154.
This code was found by Heurico 1.13 in 347 seconds.