The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+38x^22+50x^23+82x^24+44x^25+32x^26+2x^27+5x^28+1x^30+1x^34

The gray image is a code over GF(2) with n=192, k=8 and d=88.
This code was found by Heurico 1.16 in 3.81e-009 seconds.