The generator matrix

 1  0  0  0  0  1  1  1  1  2  1  1  1  1  X X+2  0  1  X  1
 0  1  0  0  0  2  1  3 X+1  1  X  X  X X+1  1 X+2  1 X+2  X  2
 0  0  1  0  0 X+3 X+1 X+2 X+2 X+3  2  X  3  0  3  1 X+2  2  1  2
 0  0  0  1  0  1  X  3  0  3  2 X+3  1 X+1  0  X X+3  1 X+1  0
 0  0  0  0  1  1  2 X+2  3 X+3  1 X+2  2 X+1  3 X+1 X+1 X+1  X  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+186x^14+546x^15+1212x^16+2444x^17+3629x^18+5416x^19+5746x^20+5536x^21+3804x^22+2458x^23+1085x^24+452x^25+189x^26+44x^27+20x^28

The gray image is a code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.13 in 2.97 seconds.