The generator matrix

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

generates a code of length 14 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+100x^11+150x^12+544x^13+480x^14+536x^15+127x^16+96x^17+4x^19+10x^20

The gray image is a code over GF(2) with n=112, k=11 and d=44.
This code was found by Heurico 1.16 in 0.016 seconds.