The generator matrix
1 0 1 1 1 X^2+X+2 1
0 1 1 X^2+2 X+3 1 0
0 0 X X^2+X X^2 X^2 0
0 0 0 2 0 2 2
generates a code of length 7 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+38x^4+142x^5+824x^6+2090x^7+825x^8+130x^9+40x^10+6x^11
The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 3.81e-009 seconds.