The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+5x^12+58x^13+7x^14+44x^15+2x^16+10x^17+1x^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 -1.01e-007 seconds.