The generator matrix

 1  0  0  1  1  1 X^2+X X^3+X^2  1 X^3  1  0  1  1  1  1  1  X  1 X^3+X  1 X^2+X  1 X^2 X^3  1  1  1  1  1  1  1  0 X^3+X^2+X X^3+X^2  1  1 X^2+X  0 X^3+X^2 X^3+X^2+X  1
 0  1  0  0  1 X^3+X+1  1  1 X^2+X  X X^2+X  1 X^3+1 X^3+1 X^2 X^3 X^3+X+1  1 X^2 X^2+X X^2+1  1 X+1  1 X^2 X^3+X^2+X  X X^3 X^2+X+1 X+1 X+1  1  1  1  1  X X^3+X^2  1  1 X^3 X^3+X^2+X  0
 0  0  1  1  1 X^2+X  1 X^3+1 X^3+1  1 X^2+X X^3+X^2+X X^3+X^2+1 X^3  X X^3+X^2+X+1 X+1 X^3+X^2+X+1 X^2+1  1 X^2+X X^3+X X^3+1 X^3+X+1  1 X^3+X^2+X+1 X^3+X^2 X^2  0 X^2  0 X^3+X^2+X+1 X^2 X^3+X^2+X+1 X^3+X^2 X^3+X X^2+X+1 X+1 X^2+X  1  1  0
 0  0  0  X X^3 X^3+X X^3+X X^3+X^2 X^2 X^3+X X^2+X X^3+X X^3+X^2+X X^3+X^2 X^3 X^3+X^2+X  0  X X^2  X X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2+X X^2+X X^3+X  0 X^2+X X^2+X X^3+X^2+X X^3 X^2  0  0 X^2+X X^3+X^2+X  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+85x^36+630x^37+1521x^38+2458x^39+3854x^40+5254x^41+5588x^42+4956x^43+3795x^44+2420x^45+1283x^46+570x^47+227x^48+78x^49+22x^50+16x^51+6x^52+2x^53+2x^54

The gray image is a linear code over GF(2) with n=336, k=15 and d=144.
This code was found by Heurico 1.16 in 7.13 seconds.