The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3  1  1  1  1  X  1  1  1  0  1  1  1 X^2  1  1  1  1 X^2  1  1  0  1  0
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^2 X^2+X  0 X^2+X X^3 X^3+X X^2  X X^2+X  X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X  0 X^2  X X^3+X X^3+X^2+X  0  X X^3+X^2+X X^2  0 X^3+X^2 X^2  X X^3  X X^3+X^2  X
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2 X^2  0 X^3 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2  0  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3  0  0 X^3
 0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3
 0  0  0  0 X^3  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 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 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+136x^37+117x^38+262x^39+263x^40+536x^41+307x^42+220x^43+48x^44+82x^45+23x^46+30x^47+7x^48+12x^49+2x^53+1x^56+1x^66

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 0.453 seconds.