The generator matrix

 1  1  1  1  1  1  1  0  1 X^2+2  2  1  1  X
 0  X  0  X  2 X+2  0  X  X  X X^2 X^2+2 X^2+X+2 X+2
 0  0  X  X X^2 X^2+X X^2+X  2 X^2 X^2+X  X  X  0 X^2+X

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+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 0.016 seconds.