The generator matrix

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

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+126x^21+845x^22+1828x^23+4024x^24+5434x^25+8030x^26+5812x^27+4104x^28+1592x^29+745x^30+168x^31+39x^32+14x^33+4x^34+2x^37

The gray image is a code over GF(2) with n=208, k=15 and d=84.
This code was found by Heurico 1.16 in 3.39 seconds.