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

generates a code of length 51 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+35x^48+232x^49+27x^50+448x^51+28x^52+208x^53+36x^54+8x^57+1x^98

The gray image is a code over GF(2) with n=408, k=10 and d=192.
This code was found by Heurico 1.16 in 0.141 seconds.