The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  2 X+2  1  0  X X+2  0  1 X+2
 0  1  0  0  0  1  1  1  2 X+2  3 X+3  X  1  2  1  1  1 X+2  2  1
 0  0  1  0  1  1  0  3  2  3 X+1 X+2  1 X+2 X+3 X+2 X+1  1  1 X+3 X+2
 0  0  0  1  1  2  3  1 X+1  X X+3  2  3 X+1  3 X+3  2 X+3 X+3  X  3
 0  0  0  0  2  0  2  2  2  0  2  0  0  0  0  0  2  2  0  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+149x^16+352x^17+717x^18+934x^19+1316x^20+1278x^21+1299x^22+956x^23+722x^24+284x^25+139x^26+30x^27+4x^28+6x^29+5x^30

The gray image is a code over GF(2) with n=84, k=13 and d=32.
This code was found by Heurico 1.13 in 0.251 seconds.