The generator matrix

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

generates a code of length 42 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+414x^35+1683x^36+4460x^37+9898x^38+19184x^39+30411x^40+41556x^41+45882x^42+42738x^43+30937x^44+19216x^45+9568x^46+3978x^47+1492x^48+484x^49+154x^50+48x^51+20x^52+12x^53+2x^54+6x^55

The gray image is a linear code over GF(2) with n=336, k=18 and d=140.
This code was found by Heurico 1.16 in 306 seconds.