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  X  X  1  0  1  1 X^2  0 X^2  1  1  X  1  X  1 X^2  0 X^2 X^2 X^2  1  X  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  0  0  X  X X^2+X  0  0 X^2+X  X X^2  X  X X^2 X^2+X X^2  0  X  X  X  X X^2  0  0 X^2  X  0 X^2 X^2  0  0  X  X X^2  0
 0  0  X  0  X  X  X  0 X^2  0 X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X  0 X^2  X X^2+X X^2 X^2  0  X X^2+X  X X^2 X^2  X X^2+X  X X^2  X  0  X  X  0 X^2+X  0 X^2  0
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2 X^2+X  X  0 X^2  X  X  0 X^2+X X^2 X^2 X^2+X  0  X  0 X^2+X  0  X X^2+X X^2+X X^2  X X^2+X  0 X^2+X  X  0 X^2  X X^2+X  0 X^2+X  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2  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+44x^38+74x^39+125x^40+130x^41+167x^42+204x^43+197x^44+258x^45+195x^46+180x^47+132x^48+90x^49+84x^50+44x^51+47x^52+30x^53+16x^54+10x^55+10x^56+4x^57+5x^58+1x^62

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 0.225 seconds.