The generator matrix

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

generates a code of length 43 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+82x^38+216x^39+345x^40+506x^41+704x^42+576x^43+649x^44+396x^45+275x^46+152x^47+82x^48+58x^49+24x^50+16x^51+11x^52+2x^54+1x^62

The gray image is a linear code over GF(2) with n=344, k=12 and d=152.
This code was found by Heurico 1.16 in 0.235 seconds.