The generator matrix

 1  0  0  0  1  1  1  2  1  2  1 X+2  1  1  1  1 X+2  2 X+2  1
 0  1  0  0  0  1  1  1 X+3  1  2  X  3 X+1  X  0  1  X  1  0
 0  0  1  0  1  1  X X+1  X X+3  0  1  0 X+2 X+1  3  2  1 X+1  0
 0  0  0  1  1  0 X+1  1  X  2 X+3  3 X+3 X+2  1 X+2  3  0  1  0
 0  0  0  0  X  2  0  2  X  X X+2  0  X  2  0 X+2  0  X X+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+104x^14+350x^15+648x^16+1292x^17+1971x^18+2364x^19+2744x^20+2640x^21+1984x^22+1230x^23+629x^24+276x^25+99x^26+40x^27+10x^28+2x^30

The gray image is a code over GF(2) with n=80, k=14 and d=28.
This code was found by Heurico 1.13 in 0.802 seconds.