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  0  1  1 X+2  1  1 2X+2  1  1  1  X  1  1  1  X 2X+2 2X+2  1  1 3X+2  1  2  1  0 2X
 0  1 X+1 X+2  3  1 3X+3 2X+2  1 3X 2X+1  1  0 X+1  1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2 2X+1  1 2X+2 3X+1  1  2 3X  X 2X+2 3X+2 2X+2  3 X+2  1  X 3X+3 X+3  1  2  1 2X+2  X  X
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0 2X  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0 2X  0 2X  0 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0 2X  0 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+461x^48+588x^50+607x^52+304x^54+75x^56+4x^58+5x^60+2x^64+1x^80

The gray image is a code over GF(2) with n=408, k=11 and d=192.
This code was found by Heurico 1.16 in 112 seconds.