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

generates a code of length 43 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+436x^36+1684x^37+5124x^38+10264x^39+18556x^40+30804x^41+40304x^42+46088x^43+42268x^44+31004x^45+19208x^46+10060x^47+4025x^48+1484x^49+560x^50+176x^51+56x^52+16x^53+20x^54+4x^55+2x^56

The gray image is a linear code over GF(2) with n=344, k=18 and d=144.
This code was found by Heurico 1.16 in 316 seconds.