The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1 X^2  0  X  1  1  1 X^3+X^2  X  1  1  1 X^3  X  X  1  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2 X^3+X^2+X  X X^3+X^2  X X^3+X^2+X X^3+X X^2  X X^2+X X^3+X X^3+X^2 X^3+X^2  X X^3  0  X X^2+X X^2+X  0  X  X X^3+X^2 X^2+X X^3+X X^3 X^3+X X^3+X^2 X^2+X X^3
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2  X X^2  X X^3+X^2+X X^3+X^2+X X^3+X  0 X^3 X^3 X^3+X X^2 X^3+X^2+X X^2  0  X  X X^3+X^2 X^2  X  0  X X^2+X  X X^3 X^3+X^2+X X^3  0 X^2+X X^3+X^2+X X^3
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^2  0 X^2 X^2 X^3+X^2  0 X^3 X^3 X^3+X^2 X^3 X^3 X^2 X^3  0 X^3 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0 X^2 X^2 X^2 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+104x^38+162x^39+374x^40+512x^41+591x^42+768x^43+561x^44+444x^45+262x^46+116x^47+99x^48+32x^49+48x^50+8x^51+5x^52+4x^53+2x^55+2x^58+1x^66

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 0.234 seconds.