The generator matrix

 1  0  0  0  1  1  1  2  1  1 X+2  1  2  1  2  X  1  1  1 2X+2  2 X+2 3X  1  1
 0  1  0  0 2X+2 2X+1  3  1 3X+2 3X+3  1 X+2 3X+2 3X+1  1  1  2  3  2  1  1 X+2  1  3 2X
 0  0  1  0 2X+3  1 2X+2 2X+3  0 2X 3X+2 3X+3  1  3 X+3  2 3X+3 3X+2  X X+2  3  1 X+2 2X+3 2X+2
 0  0  0  1  1 2X+2 2X+3 2X+3 X+1  X  1 2X 2X+3 3X+3  0  3 3X+2 3X+2  X  X X+3  X 2X+2 X+2 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+213x^20+1358x^21+3408x^22+7800x^23+12509x^24+14942x^25+12530x^26+7952x^27+3351x^28+1130x^29+236x^30+88x^31+6x^32+10x^33+2x^34

The gray image is a code over GF(2) with n=200, k=16 and d=80.
This code was found by Heurico 1.16 in 10.8 seconds.