The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  1  1  0 X^2+X  1  1  1  1 X^2+2 X+2  1  1  1  1  X  X
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X^2+X X+1 X^2+1  1  1 X^2+2 X+2 X+1 X^2+1  1  1  0  2 X+2  X X^2+X+2  X
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  0  2  2  2  2  2  2  0  0  2  2  0  0  0  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  0  0

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+338x^28+368x^30+293x^32+16x^34+6x^36+2x^40

The gray image is a code over GF(2) with n=240, k=10 and d=112.
This code was found by Heurico 1.16 in 9.55 seconds.