The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+242x^20+1536x^21+5140x^22+13678x^23+31452x^24+47966x^25+60884x^26+49780x^27+31772x^28+12956x^29+4812x^30+1494x^31+339x^32+70x^33+12x^34+8x^35+2x^36

The gray image is a code over GF(2) with n=208, k=18 and d=80.
This code was found by Heurico 1.16 in 168 seconds.