The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+52x^13+147x^14+266x^15+519x^16+1080x^17+1882x^18+2634x^19+3090x^20+2832x^21+1892x^22+1022x^23+528x^24+248x^25+110x^26+46x^27+22x^28+12x^29+1x^30

The gray image is a code over GF(2) with n=80, k=14 and d=26.
This code was found by Heurico 1.16 in 2.17 seconds.