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

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+110x^48+128x^50+512x^51+224x^52+48x^56+1x^96

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 2.13 seconds.