The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+138x^23+591x^24+1102x^25+1513x^26+1624x^27+1589x^28+864x^29+474x^30+206x^31+48x^32+34x^33+5x^34+3x^36

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.