The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+62x^46+218x^47+393x^48+524x^49+507x^50+718x^51+560x^52+520x^53+306x^54+166x^55+69x^56+24x^57+15x^58+2x^59+4x^65+5x^66+1x^72+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 0.25 seconds.