The generator matrix

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

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+152x^43+745x^44+1610x^45+2815x^46+3982x^47+4589x^48+4988x^49+4967x^50+3974x^51+2431x^52+1406x^53+698x^54+236x^55+100x^56+24x^57+31x^58+6x^59+6x^60+4x^61+1x^62+2x^63

The gray image is a linear code over GF(2) with n=392, k=15 and d=172.
This code was found by Heurico 1.16 in 9.16 seconds.