The generator matrix

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

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+137x^46+256x^47+344x^48+494x^49+570x^50+652x^51+527x^52+404x^53+319x^54+160x^55+111x^56+54x^57+36x^58+20x^59+8x^61+2x^62+1x^76

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 0.313 seconds.