The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  0  X  1  1  X  X  X  1
 0  X  0  X  0  0  X X+2  0  2  X X+2  X X+2  X  2  0  X  0  0
 0  0  X  X  0 X+2  X  0  2  X  X  0  0  2  X  2 X+2 X+2 X+2  0
 0  0  0  2  0  0  0  2  2  2  0  2  0  0  0  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  0  2
 0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  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+35x^14+48x^15+103x^16+128x^17+217x^18+336x^19+313x^20+336x^21+231x^22+128x^23+83x^24+48x^25+27x^26+11x^28+2x^30+1x^32

The gray image is a code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.0524 seconds.