The generator matrix
1 1 1 1 1 1 1 1 1 X X 1 X X X 1 X 1 X 1 1
0 X 0 0 0 X X+2 X 0 0 2 2 X+2 X+2 X 2 X+2 2 0 X+2 X+2
0 0 X 0 X X X+2 0 0 X 2 X X X X X 0 2 X+2 X 0
0 0 0 X X 0 X+2 X 2 X X+2 0 X X+2 0 X+2 2 X 2 2 0
0 0 0 0 2 0 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0
0 0 0 0 0 2 0 0 0 2 0 2 0 2 2 0 0 2 0 2 0
0 0 0 0 0 0 2 0 2 2 2 0 0 2 2 0 0 0 2 2 2
0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 0 0 2 0 2
generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+100x^14+409x^16+96x^17+931x^18+384x^19+1630x^20+1088x^21+1598x^22+384x^23+1044x^24+96x^25+300x^26+114x^28+14x^30+2x^32+1x^34
The gray image is a code over GF(2) with n=84, k=13 and d=28.
This code was found by Heurico 1.16 in 0.824 seconds.