The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 1 1 1 2 1 2 X 1 1
0 2X+2 0 2X+2 0 2X+2 0 2 2X 2X+2 0 0 2X+2 2X+2 2X+2 2X+2 0 2X 0 2X 2X 2X+2 2X+2 2X+2 2X+2 2 0
0 0 2X 0 0 0 0 0 2X 0 0 2X 2X 0 0 2X 0 2X 0 0 0 2X 2X 2X 2X 2X 0
0 0 0 2X 0 0 0 2X 0 0 0 0 0 2X 0 2X 2X 2X 2X 2X 0 2X 0 2X 2X 0 0
0 0 0 0 2X 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 0 0 2X 2X 2X 0 0 2X
0 0 0 0 0 2X 0 2X 0 2X 2X 2X 0 0 0 2X 2X 0 0 0 2X 0 2X 0 2X 2X 0
0 0 0 0 0 0 2X 0 2X 0 2X 0 2X 2X 2X 0 0 2X 2X 0 2X 2X 2X 0 2X 0 2X
generates a code of length 27 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+64x^22+132x^24+192x^25+193x^26+896x^27+197x^28+192x^29+116x^30+51x^32+6x^34+2x^36+4x^38+1x^42+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.