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

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+18x^38+60x^39+77x^40+196x^41+365x^42+184x^43+49x^44+36x^45+28x^47+4x^49+1x^50+4x^53+1x^76

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 0.063 seconds.