The generator matrix

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

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+48x^47+650x^48+472x^49+868x^50+408x^51+690x^52+280x^53+320x^54+120x^55+181x^56+16x^57+36x^58+4x^60+2x^64

The gray image is a linear code over GF(2) with n=408, k=12 and d=188.
This code was found by Heurico 1.16 in 0.687 seconds.