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  X  0  X  0  X  0  X  0  X  2  X  0  X  0  X  2  2  X  0  X  2  X  X  2  0
 0  X  0 X+2  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X X+2  X X+2  X X+2  X X+2  X  X  X X+2  X X+2  X  X  0  X X+2  X  X  X  X  X  X  X
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  0  2  2  2  0  0  2  0  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  0  2  0  0  2  0  0  2  2  0  0  2  0  2  2  0  2  0  0  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  0  2  0  0  0  2  0  0  0

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+48x^54+92x^56+64x^58+32x^60+16x^62+1x^64+2x^80

The gray image is a code over GF(2) with n=228, k=8 and d=108.
This code was found by Heurico 1.16 in 0.0968 seconds.