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

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+588x^48+1276x^50+1678x^52+1464x^54+1502x^56+860x^58+574x^60+176x^62+69x^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 1.13 in 20.7 seconds.