The generator matrix

 1  0  0  0  1  1  1  0  1 X+2  1  1  2  0  1  1  1  X  0  1
 0  1  0  0  0  1  3  1  X  0  3 X+2  1  1 X+2 X+3  2  2 X+2  0
 0  0  1  0  1  1  0 X+1 X+1  1  X  0  1  1  X  2 X+3  0  1  0
 0  0  0  1  1  0 X+1 X+1  X X+1  X X+3  0 X+1  3 X+1 X+1  1  3  0
 0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  0  0
 0  0  0  0  0  2  2  2  0  2  0  2  2  0  0  0  2  0  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+131x^14+266x^15+772x^16+1204x^17+1890x^18+2590x^19+2591x^20+2680x^21+1943x^22+1222x^23+719x^24+212x^25+129x^26+18x^27+13x^28+2x^30+1x^34

The gray image is a code over GF(2) with n=80, k=14 and d=28.
This code was found by Heurico 1.16 in 1.86 seconds.