The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+94x^11+402x^12+776x^13+1646x^14+666x^15+357x^16+126x^17+26x^18+2x^21

The gray image is a code over GF(2) with n=112, k=12 and d=44.
This code was found by Heurico 1.16 in 0.016 seconds.