The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  X  X  X  X  X
 0  2  0  0  0  0  2  0  2  0  2  2  2  0  2  0  2  0  2  0
 0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  0  0  2
 0  0  0  2  0  2  0  2  0  2  0  0  0  0  2  2  2  2  2  2
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  2  2  0  0  0  0

generates a code of length 20 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+12x^17+10x^18+203x^20+18x^21+4x^22+3x^24+2x^26+1x^28+2x^29

The gray image is a code over GF(2) with n=160, k=8 and d=68.
This code was found by Heurico 1.16 in 0.016 seconds.