The generator matrix
1 1 1 1 1 1 1 1 X X X X 1 X X X 1 1 1 1 1 1
0 2 0 0 0 2 2 2 0 0 2 2 0 0 2 2 0 0 2 0 2 2
0 0 2 0 2 2 2 0 0 2 2 0 0 2 2 0 0 2 2 2 2 0
0 0 0 2 2 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 2
generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.
Homogenous weight enumerator: w(x)=1x^0+14x^21+103x^22+7x^24+2x^29+1x^30
The gray image is a code over GF(2) with n=176, k=7 and d=84.
This code was found by Heurico 1.16 in -3.24e-008 seconds.