The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  X  X  X X^2 X^2 X^2  X  1  1  1  1  1
 0  2  0  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  0  2  2  0  2  2  0  2  0  0  2  0
 0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  2  2  0  2  2  0  0  0  0  2  2  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+12x^29+40x^30+2x^32+4x^33+4x^34+1x^40

The gray image is a code over GF(2) with n=240, k=6 and d=116.
This code was found by Heurico 1.16 in 0 seconds.