The generator matrix
1 1 1 1 1 1 1
0 2 0 0 0 2 2
0 0 2 0 2 2 2
0 0 0 2 2 0 2
generates a code of length 7 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+7x^6+112x^7+7x^8+1x^14
The gray image is a code over GF(2) with n=56, k=7 and d=24.
This code was found by Heurico 1.16 in 1.05e-007 seconds.