The generator matrix

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

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+141x^38+810x^39+1504x^40+1908x^41+2623x^42+2660x^43+2656x^44+1740x^45+1277x^46+698x^47+181x^48+94x^49+53x^50+24x^51+8x^52+2x^54+2x^56+2x^57

The gray image is a linear code over GF(2) with n=344, k=14 and d=152.
This code was found by Heurico 1.16 in 2.95 seconds.