The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X^2 X X X
0 X^2+2 0 X^2+2 0 X^2+2 0 X^2+2 2 X^2 2 X^2 2 X^2 2 X^2 X^2+2 X^2+2 X^2+2 X^2+2 0 X^2
0 0 2 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0 2 2 0 2
0 0 0 2 2 2 2 0 0 0 2 2 2 2 0 0 0 2 2 0 0 0
generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+20x^20+64x^21+88x^22+64x^23+10x^24+8x^26+1x^32
The gray image is a code over GF(2) with n=176, k=8 and d=80.
This code was found by Heurico 1.16 in -3.24e-008 seconds.