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  X  1  1  1  X
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^2 X^2  0 X^2 X^3 X^2  0 X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^3+X^2 X^2 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^2 X^3  0 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2 X^3 X^2  0 X^3 X^3 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+48x^38+72x^40+64x^41+664x^42+64x^43+60x^44+40x^46+10x^48+1x^80

The gray image is a linear code over GF(2) with n=336, k=10 and d=152.
This code was found by Heurico 1.16 in 0.062 seconds.