The generator matrix

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

generates a code of length 25 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+114x^22+232x^23+660x^24+64x^25+646x^26+208x^27+104x^28+6x^30+8x^31+3x^32+2x^34

The gray image is a code over GF(2) with n=200, k=11 and d=88.
This code was found by Heurico 1.16 in 0.031 seconds.