The generator matrix
1 0 0 1 1 1 1
0 1 0 1 X+2 2 0
0 0 1 1 X+1 X+3 0
0 0 0 2X 0 2X 2X
generates a code of length 7 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+78x^4+318x^5+1552x^6+4298x^7+1553x^8+306x^9+80x^10+6x^11
The gray image is a code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.015 seconds.