The generator matrix

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

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+136x^34+784x^35+2377x^36+5724x^37+9163x^38+15348x^39+20263x^40+23146x^41+20145x^42+16474x^43+9279x^44+5016x^45+2053x^46+724x^47+284x^48+98x^49+39x^50+10x^51+4x^52+4x^55

The gray image is a linear code over GF(2) with n=328, k=17 and d=136.
This code was found by Heurico 1.16 in 76.3 seconds.