The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  1  1  1  X  1  0  X X^2  1  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3 X^3+X^2 X^3 X^2 X^3 X^3  0 X^3+X^2 X^3 X^2 X^3 X^3 X^2 X^2  0 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2  0  0 X^3+X^2  0 X^2 X^3 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3  0 X^3 X^2 X^3 X^3 X^3  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3+X^2 X^2 X^2  0 X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^3 X^3 X^2  0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2  0  0 X^3 X^2 X^3+X^2 X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  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+16x^39+169x^40+188x^41+426x^42+376x^43+403x^44+160x^45+104x^46+24x^47+42x^48+4x^49+26x^50+20x^52+2x^54+4x^56+1x^68

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 0.125 seconds.