The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  0  2
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2  2 X+1 2X+3 X+3 2X+1 3X  2 2X+2 3X+2 X+2  X  X
 0  0 2X  0 2X  0  0 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X
 0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0  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+306x^24+416x^26+296x^28+3x^32+2x^40

The gray image is a code over GF(2) with n=208, k=10 and d=96.
This code was found by Heurico 1.16 in 0.016 seconds.