The generator matrix

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

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+78x^20+724x^21+2893x^22+6818x^23+14451x^24+25752x^25+29681x^26+25366x^27+15076x^28+6924x^29+2364x^30+678x^31+218x^32+40x^33+5x^34+2x^35+1x^38

The gray image is a code over GF(2) with n=208, k=17 and d=80.
This code was found by Heurico 1.16 in 43.7 seconds.