The generator matrix

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

generates a code of length 25 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+64x^21+68x^22+174x^23+518x^24+450x^25+515x^26+132x^27+20x^28+60x^29+24x^30+14x^31+5x^32+2x^33+1x^42

The gray image is a code over GF(2) with n=200, k=11 and d=84.
This code was found by Heurico 1.16 in 0.063 seconds.