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

generates a code of length 42 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+163x^38+44x^39+253x^40+352x^41+514x^42+328x^43+196x^44+32x^45+79x^46+12x^47+60x^48+12x^50+1x^52+1x^68

The gray image is a linear code over GF(2) with n=336, k=11 and d=152.
This code was found by Heurico 1.16 in 0.172 seconds.