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 X^3  1  1  1  1  1  X  X  1  1 X^3+X^2  1  1 X^3  1 X^3  X  1  1
 0  X  0  X X^3  0 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3+X X^3+X^2 X^2 X^2+X X^2+X  X X^3 X^3 X^3+X^2+X X^3 X^2  X  X X^2 X^3 X^3+X^2 X^2 X^2+X X^3+X^2+X  X X^2+X  X X^3+X X^3+X^2  X X^3+X^2+X X^2  X X^2+X X^3+X
 0  0  X  X X^2 X^2+X X^2+X  0 X^3+X^2  X X^2 X^3+X^2+X X^2 X^3 X^2+X X^3+X X^2+X  X X^2 X^3+X^2+X X^3+X^2 X^3 X^3+X X^3+X X^2 X^3+X^2+X X^3+X  0 X^2 X^3+X^2+X X^2 X^2+X  0 X^3 X^3 X^3+X X^2 X^2+X  0  0 X^2 X^3+X
 0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  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+107x^38+158x^39+253x^40+338x^41+396x^42+346x^43+230x^44+82x^45+68x^46+20x^47+24x^48+12x^49+4x^50+4x^51+4x^52+1x^70

The gray image is a linear code over GF(2) with n=336, k=11 and d=152.
This code was found by Heurico 1.16 in 0.078 seconds.