The generator matrix

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

generates a code of length 20 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+242x^15+1637x^16+5424x^17+14235x^18+25940x^19+35469x^20+26874x^21+14512x^22+4906x^23+1420x^24+340x^25+51x^26+16x^27+1x^28+2x^29+2x^30

The gray image is a code over GF(2) with n=160, k=17 and d=60.
This code was found by Heurico 1.16 in 31.3 seconds.