The generator matrix
1 1 1 1 1 1 X
0 2 0 0 0 0 2
0 0 2 0 0 0 2
0 0 0 2 0 0 2
0 0 0 0 2 0 2
0 0 0 0 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+21x^4+32x^6+384x^7+67x^8+7x^12
The gray image is a code over GF(2) with n=56, k=9 and d=16.
This code was found by Heurico 1.16 in 1.05e-007 seconds.