The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+51x^38+256x^39+384x^40+686x^41+638x^42+896x^43+750x^44+1016x^45+730x^46+870x^47+613x^48+570x^49+310x^50+244x^51+66x^52+60x^53+31x^54+6x^55+6x^56+4x^57+4x^60

The gray image is a linear code over GF(2) with n=180, k=13 and d=76.
This code was found by Heurico 1.11 in 0.657 seconds.