The generator matrix

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

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+360x^43+1628x^44+3494x^45+4758x^46+8640x^47+8464x^48+10982x^49+8703x^50+8484x^51+4805x^52+3078x^53+1256x^54+640x^55+179x^56+28x^57+27x^58+4x^59+3x^60+2x^65

The gray image is a linear code over GF(2) with n=392, k=16 and d=172.
This code was found by Heurico 1.16 in 31.3 seconds.