The generator matrix
1 1 1 1 1 1 1 X X X 1 1 1 1
0 2 0 2 0 0 2 0 2 2 2 0 0 2
0 0 2 2 0 2 2 2 2 0 0 0 2 2
generates a code of length 14 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 13.
Homogenous weight enumerator: w(x)=1x^0+6x^13+51x^14+3x^16+2x^17+1x^22
The gray image is a code over GF(2) with n=112, k=6 and d=52.
This code was found by Heurico 1.16 in 3.62e-008 seconds.