The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+462x^16+1376x^17+3516x^18+6760x^19+8233x^20+7368x^21+3418x^22+1080x^23+469x^24+56x^25+24x^26+3x^28+2x^30

The gray image is a code over GF(2) with n=160, k=15 and d=64.
This code was found by Heurico 1.16 in 3.53 seconds.