The generator matrix

 1  0  0  1  1  1  2  1  1  1 X+2  1  X  X  0  0  X  1  1  1
 0  1  0  1  X X+3  1  0  2 X+1  1 X+3  1  0  1  1 X+2 X+3 X+3  0
 0  0  1  1  1  0 X+1  X X+1 X+3  0  X  1  1  X  0  2  3 X+3  0
 0  0  0  X  0 X+2  X X+2 X+2  2  0  2  2 X+2  X  0 X+2  0  2  0
 0  0  0  0  2  0  2  0  2  0  2  0  0  2  0  2  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  0  0  2  0  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+59x^14+204x^15+307x^16+756x^17+645x^18+1568x^19+1049x^20+1688x^21+647x^22+700x^23+303x^24+180x^25+55x^26+24x^27+3x^28+2x^30+1x^32

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 0.578 seconds.