The generator matrix

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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+639x^48+504x^49+984x^50+472x^51+535x^52+248x^53+328x^54+104x^55+220x^56+16x^57+40x^58+3x^60+2x^64

The gray image is a linear code over GF(2) with n=408, k=12 and d=192.
This code was found by Heurico 1.16 in 33.2 seconds.