The generator matrix

 1  0  0  1  1  1  X  1  1  1  1 X^3+X^2+X  0 X^3 X^3+X^2  1  1  1 X^3+X  1  1 X^3+X  1  1  1 X^2+X  1 X^3+X^2+X  1  1 X^3+X^2+X  0  1  X  1  0  1  X  1 X^3+X^2+X  1
 0  1  0  0 X^2+1 X^3+X+1  1 X^3+X^2+X+1 X^2+X X^3+X^2+X+1 X^2  X X^3+X^2  1  1 X^3  1 X^3+1  1 X^3+X^2 X^2+X  0 X^3+X^2  1 X^3+X^2+1  1  X  1  1 X^2+X+1  1  1 X^3+X+1 X^3+X X^3 X^3+X X^3+X^2+X+1  1  0 X^3+X  X
 0  0  1  1  1 X^2 X^2+1 X^3+X+1 X^3+1 X^3+X^2+X X^3+X  1  1 X^3+X X^2+X+1 X^3+X^2  0 X^3+X^2+X+1 X+1 X^3+X^2+X+1 X^3+X  1 X^3+X^2+X+1 X^2+1 X^3+X^2+X X^2+X  X X^3+X^2+X+1 X^3+X^2+1 X^3 X^2+X+1 X^3  0  1  X  1 X^3+X X^3 X^2+X  1  1
 0  0  0  X X^3+X X^3 X^3+X X^3+X^2+X  X X^3+X^2 X^2 X^3+X^2+X X^3+X^2+X X^3+X X^3+X^2 X^2+X X^3+X X^3 X^3 X^2+X X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^3  0 X^3+X X^3+X^2 X^2+X X^3+X  X  X X^2  0  X X^3 X^3+X X^2 X^3+X^2+X X^2+X 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+704x^36+1096x^37+2930x^38+3416x^39+5615x^40+5328x^41+5740x^42+3464x^43+2643x^44+960x^45+682x^46+64x^47+88x^48+8x^49+24x^50+5x^52

The gray image is a linear code over GF(2) with n=328, k=15 and d=144.
This code was found by Heurico 1.16 in 391 seconds.