The generator matrix

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

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+188x^27+268x^28+416x^29+380x^30+368x^31+216x^32+152x^33+28x^34+20x^35+2x^36+8x^37+1x^40

The gray image is a code over GF(2) with n=240, k=11 and d=108.
This code was found by Heurico 1.16 in 0.359 seconds.