The generator matrix
1 0 0 1 1 1 X^2+X+2 2 1 1 2 1 1 1 1
0 1 0 1 X X^2+X+1 1 1 X X+2 1 X^2+X+3 3 X^2+1 2
0 0 1 1 1 0 1 X X+1 2 X^2+1 X^2+X+1 X^2 X^2+X+1 X^2+X+2
0 0 0 X 2 X+2 X^2+X X^2+X X X^2+X X^2 X^2 0 X^2+X+2 X
generates a code of length 15 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.
Homogenous weight enumerator: w(x)=1x^0+162x^11+1055x^12+2782x^13+7268x^14+10132x^15+7485x^16+2748x^17+916x^18+170x^19+43x^20+6x^21
The gray image is a code over GF(2) with n=120, k=15 and d=44.
This code was found by Heurico 1.16 in 1.44 seconds.