The generator matrix
1 1 1 1 1 1 1 1 1 X X 0 X 1 X^2 1
0 X 0 X 2 0 X^2+X X^2+X X^2 X^2+2 X^2+X X X+2 2 X^2+2 0
0 0 X X X^2 X^2+X X^2+X 0 X^2+2 X+2 2 X^2+X X^2+X+2 0 X X^2+2
0 0 0 2 2 2 0 2 0 0 2 0 2 2 2 2
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+94x^13+266x^14+370x^15+635x^16+340x^17+236x^18+76x^19+4x^20+14x^21+10x^22+2x^23
The gray image is a code over GF(2) with n=128, k=11 and d=52.
This code was found by Heurico 1.16 in 0.063 seconds.