The generator matrix

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

generates a code of length 25 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+676x^20+2472x^21+7396x^22+13804x^23+26266x^24+29232x^25+27082x^26+14232x^27+6912x^28+2120x^29+744x^30+92x^31+33x^32+10x^34

The gray image is a code over GF(2) with n=200, k=17 and d=80.
This code was found by Heurico 1.16 in 47.5 seconds.