The generator matrix

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

generates a code of length 54 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+38x^52+176x^54+38x^56+1x^68+1x^72+1x^76

The gray image is a code over GF(2) with n=216, k=8 and d=104.
This code was found by Heurico 1.16 in 0.059 seconds.