The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+82x^23+594x^24+1022x^25+1705x^26+1584x^27+1597x^28+882x^29+502x^30+126x^31+79x^32+14x^33+1x^34+1x^36+2x^37

The gray image is a code over GF(2) with n=216, k=13 and d=92.
This code was found by Heurico 1.16 in 0.234 seconds.