The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  X X^2  1
 0  X  0  X  2 X+2  0  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2 X^2+X X^2+2  X X+2  X  X X^2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X  2  0 X^2+X X+2 X^2+2  2 X^2+X+2  0 X^2  2 X^2+X+2  X  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+59x^22+146x^23+152x^24+332x^25+143x^26+114x^27+55x^28+16x^29+4x^30+1x^34+1x^42

The gray image is a code over GF(2) with n=200, k=10 and d=88.
This code was found by Heurico 1.16 in 0.016 seconds.