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.