The generator matrix

 1  0  1  1  1  X  1  1 X^3+X^2+X  1  1 X^2+X X^3+X^2+X X^2  1  1 X^2  1  1  X  1  1  1  1 X^3+X^2+X  1  1  1  1  1  0  1  0 X^3+X^2  1  1 X^3  0  1 X^2  X  1
 0  1  1 X^2 X+1  1  X X^3+1  1 X^3+X X^2+X+1  1  1  1 X^2 X^3+X^2+1  1 X^2+1 X^3  1  X X+1 X^2+X X^3+X+1  1 X^2+X+1  1  1 X^2+X+1 X^3+X  X X^3+X^2+X  1  1 X^3 X^3+X^2  1 X^3+X^2 X^3  1  1 X^2+X
 0  0  X X^3+X X^3 X^3+X X^3+X X^3 X^3+X^2+X  0  X  0 X^3+X^2 X^2 X^3+X^2+X X^3+X^2 X^3+X X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X X^2+X X^2  X X^2+X X^2 X^2+X X^3+X^2 X^3+X^2+X X^2 X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2  X X^2+X X^3+X^2+X X^2  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+204x^39+338x^40+428x^41+274x^42+328x^43+226x^44+156x^45+50x^46+16x^47+12x^49+4x^50+4x^51+2x^52+4x^53+1x^56

The gray image is a linear code over GF(2) with n=336, k=11 and d=156.
This code was found by Heurico 1.16 in 0.437 seconds.