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

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+222x^78+8x^79+533x^80+64x^81+770x^82+172x^83+1016x^84+380x^85+1325x^86+644x^87+1544x^88+768x^89+1558x^90+792x^91+1647x^92+664x^93+1402x^94+368x^95+841x^96+160x^97+607x^98+60x^99+386x^100+12x^101+197x^102+4x^103+133x^104+56x^106+39x^108+6x^110+3x^112+1x^114+1x^120

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 45 seconds.