The generator matrix

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

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+298x^37+716x^38+1278x^39+1258x^40+1548x^41+1061x^42+916x^43+526x^44+378x^45+130x^46+46x^47+13x^48+16x^49+5x^50+2x^52

The gray image is a linear code over GF(2) with n=328, k=13 and d=148.
This code was found by Heurico 1.16 in 0.859 seconds.