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  X  X
 0 2X+2  0  2  0  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0 2X  2  2 2X  2 2X  2  2  0 2X+2 2X  0 2X  2  2 2X+2 2X+2 2X 2X+2 2X 2X  0  2 2X+2  0 2X  2 2X 2X  0 2X 2X+2  2  0
 0  0 2X+2  2  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0 2X  2  0 2X+2 2X  0 2X+2 2X+2 2X 2X 2X+2 2X+2 2X  2  0 2X+2 2X  2  0 2X+2 2X 2X+2  2 2X  2  2 2X 2X  0 2X+2 2X  2  0  2 2X+2
 0  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X  0  0  0  0 2X 2X 2X  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+114x^48+224x^50+256x^51+392x^52+36x^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 0.125 seconds.