The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+212x^21+1542x^22+3630x^23+7730x^24+11842x^25+15666x^26+11710x^27+8014x^28+3568x^29+1250x^30+258x^31+93x^32+10x^33+6x^34+2x^35+2x^36

The gray image is a code over GF(2) with n=208, k=16 and d=84.
This code was found by Heurico 1.16 in 11.9 seconds.