The generator matrix

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

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+45x^16+148x^17+446x^18+1004x^19+826x^20+1024x^21+428x^22+112x^23+22x^24+12x^25+22x^26+4x^27+2x^28

The gray image is a code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 0.062 seconds.