The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1 2X+2  1
 0  X  2 3X+2  0 3X+2  2 3X 2X X+2 2X+2 3X  2  0
 0  0 2X 2X 2X  0  0 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+11x^12+82x^13+71x^14+76x^15+12x^16+2x^17+1x^26

The gray image is a code over GF(2) with n=112, k=8 and d=48.
This code was found by Heurico 1.16 in 0 seconds.