The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+38x^17+108x^18+98x^19+218x^20+124x^21+205x^22+88x^23+97x^24+26x^25+6x^26+6x^27+4x^28+4x^29+1x^30

The gray image is a code over GF(2) with n=84, k=10 and d=34.
This code was found by Heurico 1.16 in 0.0157 seconds.