The generator matrix

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

generates a code of length 20 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+72x^14+944x^15+3151x^16+11106x^17+28637x^18+53284x^19+66899x^20+54624x^21+28626x^22+10752x^23+2994x^24+842x^25+169x^26+28x^27+11x^28+4x^29

The gray image is a code over GF(2) with n=160, k=18 and d=56.
This code was found by Heurico 1.16 in 109 seconds.