The generator matrix

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

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+158x^23+858x^24+582x^25+1144x^26+402x^27+640x^28+182x^29+96x^30+16x^31+13x^32+4x^33

The gray image is a code over GF(2) with n=208, k=12 and d=92.
This code was found by Heurico 1.16 in 0.062 seconds.