The generator matrix

 1  0  0  1  1  1  2  0 2X  2  1  1  1 3X 3X  1  1  X  1 X+2 X+2 2X+2 3X+2  1  1  1
 0  1  0 2X+2 2X+3  1  1 3X+2  1  1  2 3X+2 X+3  1  1  2 X+2  1 3X+1  1  1  1 3X X+1  3  0
 0  0  1 3X+3 X+1 2X+2 X+1  1 X+2 2X+1 3X+2 2X+3 X+1 3X+2 3X+1 2X+3 2X+2  X  2  3  2 3X+3  1  2  3  0
 0  0  0 2X 2X  0 2X 2X 2X  0  0  0  0 2X  0 2X 2X  0 2X 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+161x^22+506x^23+1054x^24+1656x^25+1631x^26+1556x^27+886x^28+464x^29+207x^30+34x^31+25x^32+8x^33+1x^34+2x^36

The gray image is a code over GF(2) with n=208, k=13 and d=88.
This code was found by Heurico 1.16 in 0.219 seconds.