The generator matrix

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

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+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 code over GF(2) with n=408, k=12 and d=184.
This code was found by Heurico 1.16 in 0.234 seconds.