The generator matrix
1 0 0 1 1 1 X+2 1 1 1 1 1 1 1 1
0 1 0 X X^2+1 X+3 1 X^2 X^2+X+1 X+2 1 1 X+2 X^2+X X^2+X
0 0 1 1 X+1 0 1 X^2+X X X^2+X+1 X+1 X X^2+1 X+2 X^2+1
0 0 0 X^2 2 X^2+2 X^2+2 X^2 2 X^2+2 X^2 X^2+2 2 X^2 0
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+86x^11+482x^12+1444x^13+3614x^14+5052x^15+3816x^16+1352x^17+392x^18+126x^19+12x^20+4x^21+2x^22+1x^24
The gray image is a code over GF(2) with n=120, k=14 and d=44.
This code was found by Heurico 1.16 in 0.39 seconds.