The generator matrix

 1  1  1  1  1  1  1  1  X  0  X 2X+2  1  1
 0  X 2X+2 X+2 2X 3X+2  2 3X X+2  X 3X  X  0 2X+2

generates a code of length 14 over Z4[X]/(X^2+2) 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 -1.01e-007 seconds.