The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  1  X  X  X  X  X  X  X  X  X
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2 X^2+2 X^2+2 X^2+2  0  2  2 X^2  0  0  2 X^2 X^2+2 X^2  2  0
 0  0  2  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  0  2  2  2  0  2  0  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  2  2  0  2  0  2  2  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+14x^25+26x^26+176x^27+30x^28+6x^30+1x^32+2x^41

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 0.61 seconds.