The generator matrix

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

generates a code of length 42 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+69x^36+80x^38+225x^40+512x^41+288x^42+512x^43+214x^44+80x^46+57x^48+5x^52+4x^56+1x^72

The gray image is a linear code over GF(2) with n=336, k=11 and d=144.
This code was found by Heurico 1.16 in 0.125 seconds.