The generator matrix

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

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+34x^39+262x^40+172x^41+237x^42+50x^43+143x^44+48x^45+51x^46+16x^47+8x^48+1x^52+1x^60

The gray image is a linear code over GF(2) with n=336, k=10 and d=156.
This code was found by Heurico 1.16 in 0.281 seconds.