The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+392x^16+448x^17+2170x^18+768x^19+3312x^20+1664x^21+4240x^22+768x^23+1668x^24+448x^25+500x^26+3x^32+2x^34

The gray image is a code over GF(2) with n=84, k=14 and d=32.
This code was found by Heurico 1.16 in 2.93 seconds.