The generator matrix

 1  0  1  1  1  2 X^2+X  1  1  1 X^2+X+2  1  1  1  1 X^2  1 X+2  1  1  1  1  X  X  1  0  X  1  X X^2+X
 0  1 X+1 X^2+X+2 X^2+1  1  1  2 X^2+3 X^2+X  1  3 X^2+X+1 X+1 X^2  1 X+2  1  X X^2+2 X^2+X+3  1  1 X^2+X+2 X^2  0  0 X^2+X X^2  1
 0  0 X^2 X^2+2  2 X^2  0 X^2 X^2+2  0 X^2+2  2 X^2+2  0 X^2 X^2  2  2 X^2+2  2  0 X^2 X^2+2 X^2 X^2+2 X^2  0 X^2+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+258x^28+216x^29+224x^30+88x^31+119x^32+72x^33+32x^34+8x^35+4x^36+2x^44

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 46.7 seconds.