The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+232x^21+1496x^22+3848x^23+7285x^24+12280x^25+14872x^26+12852x^27+7527x^28+3496x^29+1240x^30+288x^31+82x^32+24x^33+8x^34+4x^35+1x^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 12.2 seconds.