The generator matrix

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

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+18x^38+176x^39+135x^40+128x^41+348x^42+448x^43+364x^44+88x^45+146x^46+168x^47+11x^48+8x^49+8x^51+1x^72

The gray image is a linear code over GF(2) with n=344, k=11 and d=152.
This code was found by Heurico 1.16 in 0.109 seconds.