The generator matrix
1 1 1 1 1 1 1 1 X 0 X X^2+2 1 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 X^2+X X X+2 X 0 X^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+40x^13+44x^14+40x^15+1x^16+2x^20
The gray image is a code over GF(2) with n=112, k=7 and d=52.
This code was found by Heurico 1.16 in -6.48e-008 seconds.