The generator matrix

 1  0  0  1  1  1 2X+2  1  1  0 2X+2 2X  1  1 X+2  1  1  X  1  1 3X X+2  1  1  2
 0  1  0  0  3  3  1 2X 2X+3 3X+2  1  1  X X+3  1  X 3X  1 X+2 X+1 2X+2  1 2X+1 3X+2  1
 0  0  1 X+1 3X+3 2X+2 3X+3 X+2 2X+1  1  1 X+2 3X+3  0  X  X 2X+1 2X 3X+1 3X+1  1 3X+1  X 2X+3 3X
 0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0  0 2X 2X  0  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+653x^22+1096x^23+1395x^24+2056x^25+1300x^26+1048x^27+518x^28+24x^29+93x^30+6x^32+2x^34

The gray image is a code over GF(2) with n=200, k=13 and d=88.
This code was found by Heurico 1.16 in 17.8 seconds.