The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1  1 X^2+X X^3+X  1  1 X^3+X^2  1  1  1  1 X^3+X  1  1  0  1  1  0 X^3+X  1  1  1  1  0 X^2+X X^3 X^3+X^2 X^3+X^2  X  X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+1 X^3+X  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  1 X+1 X^2+X  1 X^3+X^2+X X^2+1 X^3+X^2+X+1  0  1 X^3+X^2 X^2+1  1 X^3+X X^3+X^2  1  1 X^3+1 X^2+1 X+1 X^2+X  1  1  1  1  1  0 X^3+X^2
 0  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  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+91x^46+228x^47+331x^48+488x^49+547x^50+764x^51+535x^52+464x^53+317x^54+220x^55+88x^56+8x^57+3x^58+4x^59+2x^60+2x^66+3x^68

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 0.25 seconds.