The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 2 0 0 0 2 0 0 2 2 0 0 2 2 2 2 0 0 0 0 2
0 0 2 0 0 2 0 2 2 0 2 2 2 2 0 0 0 0 0 2 2
0 0 0 2 0 2 2 2 0 0 2 0 0 2 2 2 0 0 2 2 0
0 0 0 0 2 2 2 0 0 2 2 2 2 0 0 2 0 2 2 0 0
generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+5x^18+10x^20+96x^21+10x^22+5x^24+1x^42
The gray image is a code over GF(2) with n=84, k=7 and d=36.
This code was found by Heurico 1.16 in 0.00234 seconds.