The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3+X^2  1  1  1  1 X^3  1  1 X^3+X^2+X  1  1 X^2+X  1 X^2  1 X^3+X  1  1  1 X^2  1  1  1  1  1  1  1  1  1 X^3  1  1  X
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X^2+X X^2+1  X X^3+1  1 X^3+X+1  0  1 X^3+X  1  1 X^3  1 X^2+1  1 X^2 X^3+1 X^3+X  1 X^2+X+1 X+1 X+1 X+1 X^3+X^2+1 X^3 X^3+X^2+X X^3+X^2+X X^2  X  0 X^2+X X^2+X
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2  0 X^2 X^2  0 X^3 X^3+X^2 X^3  0 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2
 0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0
 0  0  0  0 X^3  0 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 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 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+271x^38+232x^39+608x^40+544x^41+845x^42+528x^43+577x^44+224x^45+217x^46+8x^47+27x^48+3x^50+2x^52+8x^54+1x^60

The gray image is a linear code over GF(2) with n=336, k=12 and d=152.
This code was found by Heurico 1.16 in 0.969 seconds.