The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  0  2  X  0  0  2  0  X  X  0  0  X  X
 0  2  0  0  0  2  2  2  0  0  0  2  0  2  2  2  0  0  0  2  2  0  2  2  0  0  2  0  2  2  2  0  0  0  2  0  2  0  2  2  0  2  2  0  2  2  2  2  0  0  0  0  2  2
 0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  0  2  2  0  2  0  2  2  2  0  0  0  0  2  2  2  2  2  2  0  2  0  2  0  2  2  0  0  2  2  2  2  2  2
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  0  2  2  0  2  0  2  2  2  0  0  2  2  0  0  2  2  0  0  0  2  2  0  2  0  2  0  2  0  0  2  0  2

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

Homogenous weight enumerator: w(x)=1x^0+52x^54+2x^56+4x^58+4x^60+1x^64

The gray image is a code over GF(2) with n=216, k=6 and d=108.
This code was found by Heurico 1.16 in 1.1 seconds.