The generator matrix
1 0 0 1 1 1 X^2+2 1 1 1 X^2+X X+2 X^2+X 1 X+2 X+2
0 1 0 X^2 X^2+1 X+3 1 X^2+X 1 X+3 X^2+X 1 1 2 0 X^2+X
0 0 1 X^2+X+1 X+1 X^2 X^2+1 X+1 1 X 1 X^2+1 0 X+3 1 1
0 0 0 2 2 2 2 0 0 0 2 0 2 0 2 0
generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 13.
Homogenous weight enumerator: w(x)=1x^0+268x^13+958x^14+1520x^15+2739x^16+1544x^17+860x^18+240x^19+44x^20+12x^21+6x^22
The gray image is a code over GF(2) with n=128, k=13 and d=52.
This code was found by Heurico 1.16 in 0.75 seconds.