The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+259x^16+296x^17+540x^18+624x^19+712x^20+576x^21+560x^22+272x^23+192x^24+24x^25+36x^26+4x^28

The gray image is a code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.11 in 0.0691 seconds.