The generator matrix

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

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+120x^22+858x^23+688x^24+1052x^25+421x^26+650x^27+203x^28+80x^29+3x^30+16x^31+4x^32

The gray image is a code over GF(2) with n=200, k=12 and d=88.
This code was found by Heurico 1.16 in 0.046 seconds.