The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  2 X^2  2 X^2  2 X^2  0
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  2  2  0  2  0  2  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  2  0  0  2  2  0  2  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  2  2  0  2  2  2  0  0  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+20x^22+46x^24+384x^25+40x^26+16x^28+4x^30+1x^48

The gray image is a code over GF(2) with n=200, k=9 and d=88.
This code was found by Heurico 1.16 in 0.016 seconds.