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

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+64x^79+122x^80+174x^81+268x^82+280x^83+347x^84+420x^85+442x^86+562x^87+530x^88+624x^89+698x^90+588x^91+644x^92+516x^93+410x^94+374x^95+271x^96+210x^97+157x^98+128x^99+89x^100+72x^101+48x^102+38x^103+36x^104+32x^105+20x^106+12x^107+8x^108+4x^110+2x^111+1x^130

The gray image is a linear code over GF(2) with n=360, k=13 and d=158.
This code was found by Heurico 1.16 in 9.09 seconds.