The generator matrix

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

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+118x^37+149x^38+220x^39+372x^40+392x^41+365x^42+190x^43+120x^44+62x^45+9x^46+32x^47+2x^48+4x^49+3x^50+6x^51+2x^54+1x^64

The gray image is a linear code over GF(2) with n=328, k=11 and d=148.
This code was found by Heurico 1.16 in 3.5 seconds.