The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3+X^2  1  1  1  1  1  1 X^2 X^2  1  1  1  1 X^3 X^3  X  X  X X^3  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2+X X^3+X^2  X X^3+X^2 X^2+X X^3+X^2+X X^3 X^3 X^3+X^2+X  X X^2+X X^2+X X^3+X X^2 X^2+X X^2  X X^3+X^2 X^2+X X^2 X^2 X^3  X  X X^3+X^2+X X^2  0 X^3 X^2+X
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2  X  X X^3+X^2+X X^3+X  X X^3+X X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  X X^2 X^3+X  X  X X^2+X  0 X^3  0 X^3+X^2  0  X  X X^3+X  X X^3+X
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^2 X^3  0 X^3+X^2 X^3 X^3 X^2 X^3 X^3+X^2  0  0 X^3 X^2  0 X^2 X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 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+426x^38+104x^39+688x^40+416x^41+948x^42+400x^43+616x^44+96x^45+268x^46+8x^47+102x^48+20x^50+2x^54+1x^64

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 59.4 seconds.