The generator matrix
1 1 1 1 1 1 1 1 X 0 X X^2+2 X 2 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 X^2+X X X+2 X X^2+X+2 X 0
generates a code of length 15 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+30x^14+64x^15+30x^16+1x^18+1x^20+1x^22
The gray image is a code over GF(2) with n=120, k=7 and d=56.
This code was found by Heurico 1.16 in 0.016 seconds.