The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+92x^15+477x^16+648x^17+764x^18+1228x^19+1632x^20+1488x^21+760x^22+532x^23+434x^24+104x^25+12x^26+4x^27+16x^28

The gray image is a code over GF(2) with n=80, k=13 and d=30.
This code was found by Heurico 1.16 in 46.8 seconds.