The generator matrix

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

generates a code of length 27 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+27x^22+70x^23+70x^24+120x^25+426x^26+664x^27+414x^28+114x^29+47x^30+30x^31+23x^32+20x^33+12x^34+4x^35+3x^36+2x^37+1x^44

The gray image is a code over GF(2) with n=216, k=11 and d=88.
This code was found by Heurico 1.16 in 0.047 seconds.