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

generates a code of length 43 over Z2[X]/(X^4) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+134x^37+648x^38+1434x^39+2795x^40+3520x^41+5495x^42+4972x^43+5344x^44+3534x^45+2672x^46+1316x^47+598x^48+156x^49+95x^50+36x^51+14x^52+2x^54+2x^55

The gray image is a linear code over GF(2) with n=344, k=15 and d=148.
This code was found by Heurico 1.16 in 8.09 seconds.