The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  X  X  1
 0  X  2 3X+2  0 3X+2  2 3X  0 3X+2  2 3X  0 2X 3X+2 X+2  2 3X+2 3X+2  0
 0  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0  0
 0  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0
 0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 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+24x^16+68x^17+21x^18+256x^19+299x^20+248x^21+8x^22+64x^23+27x^24+4x^25+2x^26+1x^28+1x^34

The gray image is a code over GF(2) with n=160, k=10 and d=64.
This code was found by Heurico 1.16 in 6.87e-008 seconds.