The generator matrix

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

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+34x^46+176x^47+443x^48+626x^49+561x^50+488x^51+558x^52+580x^53+399x^54+152x^55+29x^56+18x^57+14x^58+8x^61+7x^62+1x^64+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 0.234 seconds.