The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  1  X  1
 0 X^2+2  0  0  2 X^2+2 X^2+2 X^2 X^2 X^2  0  2  0  0
 0  0 X^2+2  0 X^2+2 X^2+2 X^2  2 X^2 X^2+2  2  0  0 X^2
 0  0  0 X^2+2 X^2  2 X^2 X^2  0  2  2 X^2 X^2+2 X^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+19x^10+34x^11+44x^12+98x^13+637x^14+92x^15+51x^16+28x^17+13x^18+2x^19+2x^21+3x^22

The gray image is a code over GF(2) with n=112, k=10 and d=40.
This code was found by Heurico 1.16 in -3.24e-008 seconds.