The generator matrix
1 0 0 1 1 1 X+2 1 1 X^2+2 1 X^2+X 1 1
0 1 0 X^2 1 X+3 1 X+2 X^2+3 1 0 1 1 X+2
0 0 1 X^2+X+1 1 X^2 X^2+1 X^2+1 X X+1 X^2+X X^2+X X^2+X+1 3
0 0 0 2 2 2 0 0 0 2 2 2 0 2
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+210x^11+880x^12+1458x^13+3128x^14+1452x^15+827x^16+204x^17+24x^18+2x^19+4x^20+2x^21
The gray image is a code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.16 in 0.094 seconds.