The generator matrix
1 1 1 1 1 1 1 0 1 X 1 X 1 2
0 X 0 X^2+X X^2 X^2+X+2 2 X 0 X^2+X+2 X^2 X^2+X X X
0 0 X^2+2 0 X^2 X^2 X^2 2 0 X^2+2 X^2+2 2 X^2+2 X^2
0 0 0 2 2 0 0 2 2 0 0 2 0 2
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+198x^12+128x^13+384x^14+128x^15+175x^16+10x^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 3.99 seconds.