The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^3  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X X^3  X X^3+X^2 X^3+X^2+X  X  0 X^3+X^2 X^2+X X^2+X X^3 X^2 X^3+X X^3+X X^2+X  0 X^2+X  0 X^3+X^2 X^3+X^2  X X^3+X^2+X X^3 X^3 X^3+X^2 X^3+X^2+X X^2  0 X^2+X X^2 X^3+X
 0  0 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^2  0  0  0 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^2 X^3  0 X^2 X^3+X^2 X^2 X^2
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3  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+72x^39+52x^40+264x^41+296x^42+232x^43+20x^44+56x^45+8x^46+16x^47+6x^48+1x^80

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 27.7 seconds.