The generator matrix

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

generates a code of length 26 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+14x^24+128x^25+14x^26+64x^27+32x^29+1x^32+2x^34

The gray image is a code over GF(2) with n=208, k=8 and d=96.
This code was found by Heurico 1.16 in -3.24e-008 seconds.