The generator matrix
1 1 1 1 1 1 1 1 X X X X 2 1
0 X^2+2 0 X^2+2 2 X^2 2 X^2 X^2+2 X^2+2 0 0 2 0
0 0 2 2 2 2 0 0 0 2 2 0 2 0
generates a code of length 14 over Z4[X]/(X^3+2,2X) 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 0 seconds.