The generator matrix

 1  0  0  0  1  1  1  1 X^3+X  1 X^3  1 X^2+X  X  1 X^3+X^2  X  1  1  1 X^3+X^2+X  1 X^3 X^3+X  1  1  1 X^2  0  1 X^3+X^2  1  1  1  1 X^3  1 X^2 X^3+X^2+X X^3  1 X^3+X^2  1
 0  1  0  0  0 X^3 X^2+1 X^3+X+1  1 X^3+1 X^3+X X+1  1  1 X^2+X  1  X X^2  0 X+1 X^3+X^2 X^2+1 X^2+X  1 X+1 X^3+X^2+X+1 X^2+X+1  1  1  1  1 X^3+X+1 X^3+X^2+X+1 X^3+X X^3  0  1 X^3+X  1  1 X+1  0 X^2
 0  0  1  0  1 X^3+X^2+X X^2  X  X  1  1 X^3+X^2+1 X^2+X+1  1 X+1 X^3+X+1  1 X^3+X^2 X^3+X+1 X^2+X+1  1 X^3+X^2 X^3+X^2 X^3 X^3+1 X^2 X+1 X^2+X X+1 X^2+1 X^3+X^2+X+1 X^3+X X^3+1 X^3+1 X^3+X+1 X^3+X^2+X X+1  1 X^3+X+1 X^2+X X^3+X+1 X^2 X^2
 0  0  0  1  1 X+1 X^2+X+1 X^3 X+1  X X^2+X+1 X^3+X^2+X+1 X^2  1 X^2+X X+1 X^2+1 X^3+X  0  X  X X^2+X  1 X^2+X+1 X^3+X^2 X^2+X+1 X^3+X+1 X^3+X X^3 X^3+1  1  1 X^3+X^2+X X^3+X X^3+X^2  1 X+1 X^2+1 X^2+X+1 X^3+X+1  0  1  0
 0  0  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  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+90x^36+792x^37+2524x^38+5226x^39+10029x^40+14854x^41+20561x^42+22242x^43+21602x^44+14990x^45+9831x^46+5096x^47+2137x^48+716x^49+265x^50+74x^51+28x^52+6x^53+1x^54+2x^55+1x^56+2x^57+2x^58

The gray image is a linear code over GF(2) with n=344, k=17 and d=144.
This code was found by Heurico 1.16 in 77.3 seconds.