The generator matrix

 1  0  0  1  1  1  0  1  1  X X+2 X+2  1  1  X  1  0  1  X X+2
 0  1  0  1  X X+3  1  0 X+3  1  X  1 X+1  2  1  1  1  0 X+2  1
 0  0  1  1  1  0 X+3  X  X  1  1  X X+1  1  X X+3 X+1  3  0  1
 0  0  0  X  0 X+2 X+2  X  2  2 X+2  X  0  0  2  X  0 X+2  X  X
 0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  2  2  0  0
 0  0  0  0  0  0  2  2  0  2  2  2  2  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+145x^14+232x^15+756x^16+960x^17+2144x^18+2456x^19+3087x^20+2208x^21+2209x^22+1144x^23+751x^24+160x^25+107x^26+8x^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 1.91 seconds.