The generator matrix

 1  0  0  1  1  1  0  1  X  1 X+2  1  1  X X+2  2  1  2  1  1
 0  1  0  0  1  1  1 X+1 X+2 X+2  1  X X+3  1 X+2 X+2 X+1  1  X  0
 0  0  1  1  0 X+1  1  2  1 X+1  2  X  1  3  1  1  0  X  X  1
 0  0  0  X  2 X+2  X  2  X  0  X  X  0  0  0  2 X+2 X+2  2 X+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+73x^16+184x^17+332x^18+284x^19+382x^20+256x^21+252x^22+144x^23+102x^24+24x^25+8x^26+4x^27+2x^28

The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.11 in 0.0177 seconds.