The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  2 X+2  X  X  1  1  X X+2  1
 0  1  1  0 X+1  1  X X+3  1 X+2  3  1  1  1  1  0 X+2  2  1  0
 0  0  X X+2  0 X+2  X  X X+2  0  2 X+2  0  X X+2  2  0  X  2  0
 0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  2  0  2  2  2  0  0  2  2  2  0
 0  0  0  0  0  2  0  0  2  0  0  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0  2  2  2

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+30x^14+70x^15+114x^16+380x^17+352x^18+826x^19+544x^20+840x^21+360x^22+378x^23+100x^24+60x^25+24x^26+6x^27+8x^28+2x^30+1x^32

The gray image is a code over GF(2) with n=80, k=12 and d=28.
This code was found by Heurico 1.16 in 0.136 seconds.