The generator matrix

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

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+57x^38+12x^39+185x^40+40x^41+265x^42+116x^43+283x^44+176x^45+304x^46+116x^47+217x^48+40x^49+116x^50+12x^51+65x^52+23x^54+13x^56+3x^58+3x^60+1x^68

The gray image is a linear code over GF(2) with n=180, k=11 and d=76.
This code was found by Heurico 1.16 in 0.232 seconds.