The generator matrix

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

generates a code of length 25 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+274x^20+1238x^21+3694x^22+7524x^23+12181x^24+15322x^25+12599x^26+7944x^27+3412x^28+938x^29+324x^30+52x^31+20x^32+6x^33+7x^34

The gray image is a code over GF(2) with n=200, k=16 and d=80.
This code was found by Heurico 1.16 in 10.2 seconds.