The generator matrix
1 1 1 1 1 1 1 1 X 1 1 X X 1 2 0 X X 2 1 X
0 2 0 2 0 2 0 2 2 0 2 0 2 0 2 2 0 2 0 2 0
generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+12x^22+3x^24
The gray image is a code over GF(2) with n=84, k=4 and d=44.
This code was found by Heurico 1.16 in 0.00177 seconds.