The generator matrix

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

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+50x^36+124x^37+402x^38+410x^39+852x^40+522x^41+834x^42+356x^43+334x^44+84x^45+69x^46+34x^47+11x^48+2x^49+1x^50+4x^53+5x^54+1x^58

The gray image is a linear code over GF(2) with n=328, k=12 and d=144.
This code was found by Heurico 1.16 in 0.172 seconds.