The generator matrix

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

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+342x^43+784x^44+1360x^45+1248x^46+1402x^47+929x^48+856x^49+554x^50+390x^51+168x^52+116x^53+20x^54+10x^55+6x^56+4x^57+2x^58

The gray image is a linear code over GF(2) with n=376, k=13 and d=172.
This code was found by Heurico 1.16 in 1.83 seconds.