The generator matrix

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

generates a code of length 20 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+291x^16+776x^17+1770x^18+3276x^19+4088x^20+3432x^21+1772x^22+688x^23+224x^24+16x^25+42x^26+4x^27+4x^28

The gray image is a code over GF(2) with n=160, k=14 and d=64.
This code was found by Heurico 1.16 in 0.594 seconds.