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  X  1  1  1
 0 X^2+2  0  0  0 X^2 X^2+2 X^2  0  0  0  0 X^2 X^2+2 X^2 X^2+2  0  2 X^2+2 X^2  2 X^2+2  2 X^2+2  2  0 X^2+2 X^2+2  2  0 X^2 X^2+2  2  0  2 X^2  2 X^2 X^2 X^2  2  0  2 X^2 X^2  2 X^2+2 X^2+2 X^2  0 X^2+2
 0  0 X^2+2  0 X^2 X^2 X^2+2  0  0  0 X^2 X^2+2 X^2 X^2+2  0  0  2  0 X^2+2 X^2 X^2  2 X^2  2  0 X^2  2 X^2  2 X^2+2 X^2+2  0 X^2+2  2 X^2  2  0 X^2+2  2 X^2+2 X^2 X^2+2 X^2+2  0  2  2  0  2 X^2 X^2 X^2
 0  0  0 X^2+2 X^2  0 X^2+2 X^2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2  0 X^2+2 X^2+2  2  0 X^2  2  2  0  0 X^2+2 X^2 X^2+2 X^2+2 X^2  0  2 X^2+2 X^2+2  0  2 X^2 X^2 X^2+2  0  0 X^2  0 X^2  2 X^2  0 X^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+71x^48+120x^50+640x^51+135x^52+40x^54+16x^56+1x^100

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.