The generator matrix

 1  0  1  1  1 X+2  1  1 3X  1  1 3X+2 X+2 2X+2  1  1  1  1 3X  1  1  2  1  1  1  1  1 2X+2  1  1  0  1  1  1  1 2X+2  1  1  1  1  1  1  1  1  1 3X  1 2X  1  0  1
 0  1  1 2X+2 X+1  1  X 2X+1  1 3X 3X+3  1  1  1 2X+2  3 3X X+1  1 2X X+3  1 2X X+3 3X+2  3  3  1 X+1 2X+1  1 X+1 2X+1 3X+3 2X+3  1 X+2  2 3X+2 2X+2 3X+2 3X 2X 3X+1 2X  1 X+3  1 2X+1  1 2X+2
 0  0  X 3X 2X 3X 3X 2X X+2  0  X  0  2 2X+2 X+2  2 X+2 2X+2  X  2 3X+2 3X+2 3X+2 2X 2X+2  0 3X+2 3X X+2 2X+2 2X+2  X 3X+2  2  X 2X 3X  0 2X  2 X+2  2  X  2 3X  0 3X 3X+2  2 3X 2X

generates a code of length 51 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+236x^48+458x^49+282x^50+190x^51+218x^52+426x^53+184x^54+10x^55+20x^56+4x^57+12x^58+4x^60+1x^64+1x^66+1x^74

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 0.109 seconds.