The generator matrix
1 1 1 1 X X 1
0 X 0 X^2+X+2 X^2+X X^2+X 0
0 0 X^2+2 X^2 2 2 0
0 0 0 2 2 0 0
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+24x^4+90x^5+72x^6+654x^7+69x^8+86x^9+24x^10+2x^11+2x^12
The gray image is a code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in 0 seconds.