The generator matrix

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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+394x^47+715x^48+1530x^49+1097x^50+1574x^51+665x^52+980x^53+424x^54+418x^55+156x^56+138x^57+63x^58+22x^59+15x^60

The gray image is a linear code over GF(2) with n=408, k=13 and d=188.
This code was found by Heurico 1.16 in 1.52 seconds.