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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+9x^24+24x^25+22x^26+144x^27+22x^28+24x^29+9x^30+1x^54

The gray image is a code over GF(2) with n=108, k=8 and d=48.
This code was found by Heurico 1.16 in 0.00788 seconds.