The generator matrix

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

generates a code of length 42 over Z2[X]/(X^4) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+450x^39+754x^40+736x^41+653x^42+472x^43+463x^44+274x^45+129x^46+122x^47+12x^48+26x^49+2x^50+2x^52

The gray image is a linear code over GF(2) with n=336, k=12 and d=156.
This code was found by Heurico 1.16 in 0.609 seconds.