The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  1  0  1 3X+2  1  1  1  1  2  1  1  0  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2 X+1  1 2X+3  1  2 3X+2 X+3 2X+3  1 3X 3X  1  0
 0  0 2X  0  0  0  0 2X  0 2X 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X 2X  0  0  0
 0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0  0  0  0 2X
 0  0  0  0 2X  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0  0  0  0 2X
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X 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+20x^22+36x^23+254x^24+480x^25+883x^26+760x^27+881x^28+480x^29+243x^30+36x^31+12x^32+1x^34+3x^36+5x^38+1x^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 0.078 seconds.