The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2 X^2 X^2+2  0 X^2+2 X^2+2  0  2  0 X^2 X^2+2
 0  0 X^2+2 X^2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0 X^2 X^2  0 X^2+2 X^2  2  0 X^2 X^2+2 X^2  0

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+34x^25+18x^26+158x^27+6x^28+30x^29+4x^30+2x^31+2x^34+1x^40

The gray image is a code over GF(2) with n=216, k=8 and d=100.
This code was found by Heurico 1.16 in 1.05e-007 seconds.