The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  2  X  1
 0  X  0 X^2+X+2  2 X^2+X  0  X X^2+2 X^2 X^2+X+2  X  0  0
 0  0 X^2+2  0  2 X^2+2 X^2+2 X^2 X^2 X^2 X^2+2  2 X^2+2  0
 0  0  0 X^2+2 X^2+2 X^2 X^2+2  2 X^2  0  0 X^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+36x^10+84x^11+134x^12+308x^13+941x^14+300x^15+127x^16+60x^17+38x^18+16x^19+2x^20+1x^22

The gray image is a code over GF(2) with n=112, k=11 and d=40.
This code was found by Heurico 1.16 in 0.015 seconds.