The generator matrix

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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+62x^46+218x^47+393x^48+524x^49+507x^50+718x^51+560x^52+520x^53+306x^54+166x^55+69x^56+24x^57+15x^58+2x^59+4x^65+5x^66+1x^72+1x^74

The gray image is a linear code over GF(2) with n=408, k=12 and d=184.
This code was found by Heurico 1.16 in 0.266 seconds.