The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  0  1  1  X X^2+2  1  1  1  1  X  2  X X^2  X  X  X  X  X  1
 0  X X^2+2 X^2+X  2 X^2+X+2 X^2 X+2  0 X^2+X X^2+X  X X^2+2 X+2 X+2  X  2 X^2 X^2+X+2  X X^2+X+2  X  X  X  0 X^2+2  2 X^2 X^2+X  0

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+18x^29+84x^30+18x^31+2x^33+2x^34+2x^35+1x^36

The gray image is a code over GF(2) with n=240, k=7 and d=116.
This code was found by Heurico 1.16 in 0.016 seconds.