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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+60x^36+116x^37+181x^38+222x^39+290x^40+418x^41+642x^42+766x^43+925x^44+1034x^45+877x^46+830x^47+594x^48+394x^49+261x^50+194x^51+147x^52+82x^53+81x^54+36x^55+31x^56+4x^57+5x^58+1x^70

The gray image is a linear code over GF(2) with n=180, k=13 and d=72.
This code was found by Heurico 1.16 in 3.24 seconds.