The generator matrix

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

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+161x^12+208x^13+344x^14+160x^15+101x^16+16x^17+32x^18+1x^20

The gray image is a code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in 0.031 seconds.