The generator matrix

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

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+340x^22+880x^23+2267x^24+2872x^25+3814x^26+2824x^27+2163x^28+776x^29+336x^30+72x^31+32x^32+6x^34+1x^36

The gray image is a code over GF(2) with n=208, k=14 and d=88.
This code was found by Heurico 1.16 in 261 seconds.