The generator matrix

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

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+70x^16+180x^17+287x^18+576x^19+553x^20+804x^21+535x^22+568x^23+261x^24+164x^25+69x^26+8x^27+11x^28+4x^29+5x^30

The gray image is a code over GF(2) with n=84, k=12 and d=32.
This code was found by Heurico 1.16 in 0.143 seconds.