The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  X  1  X  1  X  X
 0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  0  2  0  2  2  0  0  0  0  0  2  0  2  0  0  2  0  2  2  2  2  0  0  2  2  0  2  0  2  0  2  0  2  2  0  2  0  2  0
 0  0  2  0  0  0  0  0  2  2  2  2  0  0  0  2  0  2  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  2  0  0  0  2  2  0  0  0  2  0  2  2  2  0  2  0
 0  0  0  2  0  0  0  0  2  0  0  2  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  2  2  0  2  0  2  2  0  2  0  2  0  2  0  0  2  2  0  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  0  0  2  2  2  2  2  0  0  0  2  0  0  0  0  2  0  2  2  2  0  2  2  0  0  2  0  0  0  2  0  2  2  2  0  0  0
 0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  2  0  0  2  2  0  0  0  2  2  2  2  0  2  0  2  2  2  2  2  2  2  2  2  0  2  2  0  2  2  2  2  0  2  2  2  0  0  2
 0  0  0  0  0  0  2  0  2  2  0  0  0  2  2  0  2  2  2  0  0  0  2  2  0  0  0  0  2  2  0  0  0  2  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  2  0  2  0
 0  0  0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  2  2  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  2  0  0  0  0  0  2  2  2  2  0  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+118x^48+120x^52+512x^54+216x^56+8x^60+48x^64+1x^96

The gray image is a code over GF(2) with n=216, k=10 and d=96.
This code was found by Heurico 1.16 in 3.3 seconds.