The generator matrix

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

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+114x^14+378x^15+1189x^16+2298x^17+5213x^18+7188x^19+10740x^20+10870x^21+11209x^22+7468x^23+5077x^24+2118x^25+1119x^26+388x^27+143x^28+10x^29+9x^30+2x^31+1x^32+1x^36

The gray image is a code over GF(2) with n=84, k=16 and d=28.
This code was found by Heurico 1.13 in 10.6 seconds.