The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2X+2) 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 code over GF(2) with n=408, k=12 and d=184.
This code was found by Heurico 1.16 in 0.234 seconds.