The generator matrix

 1  0  0  0  1  1  1 X^2 X^3 X^3+X^2  1  1  1  1 X^2+X X^2+X  1  1  1 X^2+X X^3  1  1 X^3+X^2+X  1 X^2  1  X  1  1  1 X^2  1  1  1  1  1  1  1  1 X^3+X^2  1
 0  1  0  0 X^3  1 X^3+1  1  1  1 X^2+X X^3+X  1 X^2+1 X^3  1 X^3+X^2 X^3+X+1 X^3+X^2+X  1 X^3+X^2+X X^2+X+1 X^3+X^2  1 X^3+X^2+X+1 X^3 X^2+X+1 X^3+X X^3+X^2+X+1 X^2+X X^2+X+1  1  0 X^3+X^2+1 X^2 X^3+X^2+1 X^3+X^2+X X^3+X^2 X^3+X^2+1 X^2+X X^3+X^2  X
 0  0  1  0 X^3+1  1 X^3 X^3+X^2+1 X^2 X^3+X+1  1 X^3  X X^3+X^2+X+1  1 X^3+X^2+1 X^2 X^3+X^2+X X^2+X+1 X^3+X^2  1 X^3+X X^2+X+1 X^3+X X^3+X^2+1  1  1 X^3+X^2 X^3 X^3+X^2+X+1 X^3+X+1 X^3+1 X^3+X^2+X X^3+X+1 X^3+X^2+X+1 X^3+X X^2+1 X^2+X X^3  X  1  X
 0  0  0  1  1 X^3 X^3+X^2+1 X^3+1  1 X^3+X X^3+X X+1 X^2+X X^3+X+1 X^2+1 X+1 X^2+X X^3+X^2 X^2+X+1 X^2+1 X^3+1 X^2+1 X^3+X  0 X^2 X^3+X+1 X^2+X+1  1  0 X^2  X X^3+X X^2 X^3+X^2+1 X^3 X^3+X+1 X^3+X^2 X^3+1 X^3+X X^2+1 X^3+1  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+152x^36+1192x^37+2799x^38+5092x^39+8031x^40+9842x^41+11295x^42+10528x^43+7559x^44+4816x^45+2668x^46+1064x^47+360x^48+86x^49+27x^50+20x^51+1x^52+3x^54

The gray image is a linear code over GF(2) with n=336, k=16 and d=144.
This code was found by Heurico 1.16 in 25.6 seconds.