The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1 2X+2  1  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X+2 2X 3X  X 3X+2 2X+2  2  1  1  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+2 2X+2 3X+2 X+1  3 3X+1 2X+3 2X 3X  2  X 3X+3 X+3 2X+1  1  1  1  1  1  1  1  1  1  0 2X  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X 2X 2X  0  0 2X  0  0 2X 2X  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0 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+38x^48+352x^49+24x^50+192x^51+24x^52+352x^53+38x^54+1x^64+2x^70

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 0.063 seconds.