The generator matrix
1 1 1 1 1 1 1 1 X X X 1 2 1 0 0 1 X X X X
0 X 0 X 0 0 X X+2 0 X X+2 0 X X X 0 X X X 0 2
0 0 X X 0 X+2 X 0 X X 0 2 X X 0 X X X X+2 0 X
0 0 0 2 0 0 0 0 0 0 0 0 2 2 0 0 2 2 2 2 0
0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 2 2 2 2 0 0
0 0 0 0 0 2 0 0 0 0 2 0 2 2 2 2 0 2 2 0 0
0 0 0 0 0 0 2 0 0 2 2 0 0 2 0 2 2 2 0 0 0
0 0 0 0 0 0 0 2 0 2 0 2 2 2 0 2 2 0 2 0 0
0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 0 0 0 0 0
generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.
Homogenous weight enumerator: w(x)=1x^0+20x^13+84x^14+118x^15+170x^16+396x^17+782x^18+892x^19+836x^20+1220x^21+1404x^22+936x^23+508x^24+388x^25+272x^26+100x^27+12x^28+24x^29+16x^30+2x^31+9x^32+2x^34
The gray image is a code over GF(2) with n=84, k=13 and d=26.
This code was found by Heurico 1.16 in 0.711 seconds.