The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3+X^2  1  1  1  1  1 X^2  1  1  1  1  1  X  1  0  X  1  X X^3+X^2  X  X  1  X  1 X^3  X  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2+X X^3+X^2  X X^3+X^2 X^2+X X^3+X^2+X X^3 X^3 X^2+X X^3+X X^3+X^2+X  X X^2+X X^2 X^3+X X^3+X X^3+X  X X^2+X X^3+X^2 X^3+X X^3 X^3+X X^2+X X^3+X^2 X^2 X^3 X^3+X^2  0  X X^3+X X^3+X^2 X^3+X^2+X X^3 X^2+X  X X^3+X^2+X X^2+X
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2  X  X X^3+X^2+X X^3+X  X X^3+X X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2  X X^2+X X^3+X^2 X^2 X^3+X^2+X X^2 X^2+X X^2+X X^2  X X^3+X^2+X X^2  X X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X X^3+X  X  X X^2+X  0  X X^3+X X^2+X
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^2  0 X^3+X^2 X^3 X^3  0 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^3 X^3 X^2  0 X^3+X^2 X^2  0  0  0 X^3+X^2  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+121x^46+228x^47+369x^48+536x^49+585x^50+628x^51+520x^52+412x^53+313x^54+180x^55+82x^56+40x^57+31x^58+20x^59+19x^60+4x^61+6x^62+1x^76

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 0.328 seconds.