The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1 X^2  1  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  2 X^2+X  0 X+2 X^2+2 X^2+X X^2+2  X  0 X^2 X^2+X X^2+2 X+2  2 X^2+X  2 X+2 X^2 X^2+X  0 X+2  2
 0  0 X^2+2  0 X^2+2 X^2  2 X^2 X^2  2  2 X^2+2 X^2 X^2+2  0  2  0 X^2 X^2+2  0 X^2  2 X^2 X^2 X^2+2 X^2  0 X^2+2  2  2
 0  0  0  2  2  0  2  2  0  2  0  2  2  0  2  0  2  0  2  0  0  2  2  2  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 27.

Homogenous weight enumerator: w(x)=1x^0+72x^27+49x^28+272x^29+288x^30+232x^31+42x^32+40x^33+16x^35+3x^36+8x^37+1x^56

The gray image is a code over GF(2) with n=240, k=10 and d=108.
This code was found by Heurico 1.16 in 0.078 seconds.