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 X^2
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  2 X^2  0 X^2+2  2 X^2  0  2 X^2+2 X^2  2 X^2  2 X^2  2  2 X^2 X^2  0  2  0  2 X^2+2 X^2  2  0 X^2+2 X^2  2
 0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  0  0  2  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  2  0  0  0  0  0  0  2  2  0  0  2  2  0
 0  0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  2  0  0  0  2  0  2  0  0  0  0  2  0  2  0  2  0  2  2  0  2  0
 0  0  0  0  2  0  2  0  0  2  2  2  2  2  0  2  2  0  0  2  2  0  0  2  0  2  0  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  0  2  2  2  2  0  0  0  2
 0  0  0  0  0  2  0  2  2  2  2  0  2  0  2  2  0  0  0  0  2  2  2  2  0  0  2  2  2  0  2  0  0  0  0  0  2  2  0  0  2  0  0  2  2  0  2  0  0  2  2

generates a code of length 51 over Z4[X]/(X^3+2,2X) 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 2.11 seconds.