The generator matrix

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

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+35x^22+70x^23+85x^24+236x^25+392x^26+426x^27+409x^28+232x^29+65x^30+42x^31+14x^32+12x^33+19x^34+6x^35+3x^36+1x^42

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.