The generator matrix

 1  0  1  1  1 X^3+X^2+X  X  1  1 X^3+X^2  1  1  1  1 X^2+X  1  1 X^3  1  1  1  1 X^2 X^3+X  1  1  X  1  1  X  1  1  1  1  X  1  1  1  1  1 X^2+X  X  1
 0  1 X+1 X^2+X X^3+X^2+1  1  1 X^3+X^2 X^2+X+1  1 X^3+X^2+X X^2+1  X X^3+1  1 X^3 X+1  1 X^2 X^3+X^2+X+1 X^3+X  1  1  1  0 X^2+X  X X^3  X X^2  0 X^3+X  0 X^3+X^2+X X^2 X+1 X^3+X^2+X+1 X^3+X+1 X^3+1 X^3+X^2+1  1  1  0
 0  0 X^2  0 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3  0 X^2 X^3 X^2 X^3+X^2 X^3  0 X^2 X^3+X^2  0  0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0 X^3 X^3 X^3  0 X^3  0 X^3+X^2  0 X^2  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 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+56x^38+178x^39+305x^40+622x^41+405x^42+1008x^43+498x^44+580x^45+153x^46+136x^47+90x^48+30x^49+21x^50+2x^51+1x^52+3x^54+2x^55+2x^58+2x^59+1x^60

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 0.188 seconds.