The generator matrix

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

generates a code of length 14 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+42x^10+168x^11+528x^12+802x^13+1040x^14+784x^15+519x^16+156x^17+38x^18+8x^19+8x^20+2x^21

The gray image is a code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.031 seconds.