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

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+58x^79+117x^80+188x^81+226x^82+284x^83+392x^84+358x^85+450x^86+636x^87+529x^88+624x^89+716x^90+574x^91+590x^92+520x^93+430x^94+364x^95+301x^96+180x^97+167x^98+140x^99+70x^100+94x^101+39x^102+40x^103+40x^104+16x^105+15x^106+10x^107+7x^108+4x^109+5x^110+6x^111+1x^132

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 8.92 seconds.