The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+174x^25+348x^26+192x^27+60x^28+132x^29+100x^30+3x^32+14x^33

The gray image is a code over GF(2) with n=216, k=10 and d=100.
This code was found by Heurico 1.16 in 23.6 seconds.