The generator matrix

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

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+322x^34+1590x^35+4457x^36+9720x^37+18485x^38+30582x^39+41809x^40+47134x^41+43035x^42+31014x^43+18619x^44+9518x^45+3791x^46+1338x^47+510x^48+154x^49+27x^50+20x^51+12x^52+2x^53+4x^54

The gray image is a linear code over GF(2) with n=328, k=18 and d=136.
This code was found by Heurico 1.16 in 297 seconds.