The generator matrix

 1  0  0  1  1  1  0 X^3 X^2 X^3+X^2  1  1  1  1 X^3+X  X  1 X^3+X  1 X^2+X  1  1  X  X  1  1  1  1  1  1  0  1 X^2 X^2+X  1 X^3+X^2 X^3+X^2+X  1 X^3+X^2 X^3  1  1
 0  1  0  0 X^2+1 X^2+1  1 X^3+X^2+X  1  1 X^3+X^2 X^3+X^2+1  1 X^3 X^2+X X^3+X^2 X^3+X+1  1 X^3+X  1 X^3+X^2+X+1 X+1  1  1 X^3 X^3+X^2+1  X X^2+X  0 X^2+X+1 X^2+X X^3+1 X^3+X^2  1  X  1 X^3+X^2 X^2+X  1  1 X^2 X^3
 0  0  1 X+1 X^3+X+1 X^3 X+1  1  X X^3+1 X^2+X  1 X^3+X X^3+X^2+1  1  1 X^2 X^2+X  X X^3+1 X^3+X^2+1 X^3+X^2+X+1 X^2+X+1 X^3 X^3+1 X^3+X^2 X^3+1 X^3+X  X X^2+X  1 X^2+1  1 X^2 X^3 X^2+1  1  0 X^3+1 X^2+1 X^3+X^2+X+1 X^3
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  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+256x^38+796x^39+1257x^40+1364x^41+1400x^42+1088x^43+904x^44+496x^45+349x^46+196x^47+44x^48+28x^49+10x^50+2x^52+1x^54

The gray image is a linear code over GF(2) with n=336, k=13 and d=152.
This code was found by Heurico 1.16 in 0.89 seconds.