The generator matrix
1 0 0 0 1 1 1
0 1 0 0 X X^2+1 0
0 0 1 0 X+1 1 0
0 0 0 1 1 X 0
0 0 0 0 2 0 2
generates a code of length 7 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 3.
Homogenous weight enumerator: w(x)=1x^0+130x^3+1002x^4+5528x^5+24085x^6+69580x^7+24085x^8+5528x^9+1002x^10+130x^11+1x^14
The gray image is a code over GF(2) with n=56, k=17 and d=12.
This code was found by Heurico 1.16 in 3.02 seconds.