The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+70x^22+160x^23+220x^24+432x^25+738x^26+904x^27+732x^28+384x^29+212x^30+144x^31+69x^32+16x^33+2x^34+8x^35+2x^38+2x^40

The gray image is a code over GF(2) with n=216, k=12 and d=88.
This code was found by Heurico 1.16 in 0.125 seconds.