The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+4x^12+28x^13+68x^14+16x^15+3x^16+4x^17+4x^18

The gray image is a code over GF(2) with n=112, k=7 and d=48.
This code was found by Heurico 1.16 in 3.81e-009 seconds.