The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  X  1  1  0  1  1  X  1  1  1 X^3+X^2+X X^3+X^2+X  1  1  1 X^3+X^2  1  1 X^3+X^2  1 X^3+X^2 X^3+X^2+X  1  1  1  1  1  1 X^2  1  1 X^2 X^3+X^2+X  1
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X^3+X X+1  1 X^2 X+1  1 X^3+X^2+X+1 X^3  1  0 X^2+1 X^3  1  1 X^3 X^3 X^3+X  1 X^3+X  X  1 X^2+X  1  1 X^3+1 X^2+X+1 X^3+1 X^2+1 X^2+X+1 X^3+X^2+1 X^3+X^2 X^3+X+1 X^2+X+1  1  1 X^3+X^2
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3+X^2+X X^3 X^3+X X^3+X^2+X X^2+X X^3+X^2 X^3+X^2 X^2 X^3+X^2+X X^2+X X^3+X^2+X X^3+X^2  X X^3+X^2 X^3+X  0 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3 X^2 X^3+X^2 X^2+X X^3+X^2 X^3+X^2+X X^2 X^3  X X^3+X^2+X X^2 X^3+X^2 X^3+X X^3+X^2  0 X^3 X^2+X
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+128x^41+414x^42+820x^43+561x^44+500x^45+440x^46+676x^47+275x^48+140x^49+72x^50+40x^51+26x^52+2x^58+1x^60

The gray image is a linear code over GF(2) with n=360, k=12 and d=164.
This code was found by Heurico 1.16 in 0.187 seconds.