The generator matrix

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

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+54x^10+48x^11+494x^12+840x^13+1214x^14+872x^15+487x^16+24x^17+42x^18+8x^19+10x^20+2x^22

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.