The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  X  1  1  1  0  1  X  1  1  X  1  1  1  1  1  1 2X  1  1  X  1  1  X  0
 0  X  0 X+2 2X+2 3X+2  2  X  0 3X+2 2X 3X+2 3X 2X+2 2X+2  X  0 X+2 3X+2  X 2X 2X+2 2X 3X  X  X 2X+2 X+2 3X+2  2 3X  X 2X  0 3X+2 2X+2  X  2 3X 2X+2  X 2X+2 3X  X  0  2 X+2  0  X 3X+2  X
 0  0  2  0 2X+2  0 2X  0 2X+2 2X+2 2X  2  2  2  0 2X+2  0 2X+2  2 2X+2  2 2X  2  0 2X  0 2X  0  2  2  0 2X 2X+2 2X  2 2X  2 2X  2 2X+2 2X  2 2X  2  0  2  0 2X+2 2X+2 2X+2 2X
 0  0  0  2  0 2X 2X 2X+2 2X+2 2X+2 2X+2  0  0 2X+2  2 2X+2 2X  0  2  0 2X 2X+2  2 2X 2X+2 2X+2 2X+2 2X+2 2X 2X+2 2X 2X  0  2  0 2X  0  2 2X+2 2X  2  0  2  0  0  0  2 2X  2  2  0
 0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0 2X  0 2X  0  0 2X  0  0 2X 2X  0  0  0 2X 2X  0  0  0  0  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+254x^46+16x^47+410x^48+192x^49+924x^50+608x^51+874x^52+192x^53+370x^54+16x^55+149x^56+68x^58+5x^60+12x^62+4x^66+1x^84

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 56 seconds.