The generator matrix

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

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+15x^28+64x^29+352x^30+64x^31+15x^32+1x^60

The gray image is a code over GF(2) with n=240, k=9 and d=112.
This code was found by Heurico 1.16 in 0.015 seconds.