The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  2 X^2+X+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+88x^13+76x^14+88x^15+1x^16+2x^20

The gray image is a code over GF(2) with n=112, k=8 and d=52.
This code was found by Heurico 1.16 in -1.01e-007 seconds.