The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+55x^22+278x^23+568x^24+792x^25+869x^26+712x^27+445x^28+220x^29+89x^30+34x^31+17x^32+12x^33+3x^34+1x^36

The gray image is a code over GF(2) with n=208, k=12 and d=88.
This code was found by Heurico 1.16 in 0.062 seconds.