The generator matrix

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

generates a code of length 25 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+96x^22+48x^23+102x^24+544x^25+104x^26+48x^27+55x^28+24x^30+1x^32+1x^44

The gray image is a code over GF(2) with n=200, k=10 and d=88.
This code was found by Heurico 1.16 in 11 seconds.