The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X 2X+2  1 2X  1  1  1  1  1
 0  X  0  X  0 2X 3X+2 2X+2 3X+2 2X+2 2X+2 3X+2  X 2X+2  X 3X+2 X+2  2 2X X+2
 0  0  X  X  2 X+2 3X+2  2 2X  0  X  0  X X+2 2X+2  X 2X+2  0 2X+2 2X+2
 0  0  0 2X  0  0  0 2X 2X 2X  0  0 2X  0  0 2X  0 2X 2X  0
 0  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X  0 2X  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+125x^16+124x^17+480x^18+648x^19+1356x^20+640x^21+480x^22+120x^23+100x^24+4x^25+16x^26+2x^32

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 0.078 seconds.