The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+574x^48+1320x^50+1700x^52+1352x^54+1516x^56+920x^58+568x^60+184x^62+53x^64+4x^68

The gray image is a code over GF(2) with n=216, k=13 and d=96.
This code was found by Heurico 1.16 in 63.7 seconds.