The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  X  1 X^3+X^2  1 X^2+X  1  1 X^3+X  1  X  1  1  1 X^3+X^2 X^2  1  1  1  1  1  1 X^2  1  1  1 X^3 X^2  1  1  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X^3+X X^3+X+1  1 X^2+1  1 X^3+X^2+X  1 X^3+X^2 X^3+X^2+X+1  1 X^2+1  1 X^3+1 X+1  X  1  1 X^3+1 X+1  0 X^3 X^2+X X^2+X+1  1 X^2+X+1 X^3+X^2+1 X^3+X+1  1  1 X^3+X+1 X^3+1 X+1 X^3+X^2
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3+X^2+X X^2  X X^2 X^2 X^3+X X^3+X^2 X^2+X X^3 X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2+X  X X^3+X^2 X^2+X X^3+X X^3 X^2+X  X X^2+X  0 X^3+X^2+X  X  X X^3+X^2 X^3  0 X^3+X X^3+X^2+X
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  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+135x^38+380x^39+593x^40+690x^41+583x^42+672x^43+544x^44+356x^45+88x^46+8x^47+18x^48+2x^49+8x^50+4x^51+12x^52+1x^58+1x^62

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 0.171 seconds.