The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+106x^23+378x^24+330x^25+525x^26+298x^27+248x^28+70x^29+50x^30+28x^31+13x^32+1x^34

The gray image is a code over GF(2) with n=208, k=11 and d=92.
This code was found by Heurico 1.16 in 0.031 seconds.