The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+60x^14+158x^15+282x^16+592x^17+919x^18+1320x^19+1583x^20+1258x^21+896x^22+622x^23+301x^24+132x^25+44x^26+12x^27+9x^28+2x^29+1x^34

The gray image is a code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.671 seconds.