The generator matrix

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

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+102x^15+806x^16+2648x^17+7090x^18+13798x^19+16548x^20+13958x^21+7196x^22+2478x^23+715x^24+160x^25+26x^26+6x^27+2x^28+2x^29

The gray image is a code over GF(2) with n=160, k=16 and d=60.
This code was found by Heurico 1.16 in 8.14 seconds.