The generator matrix

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

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+192x^27+930x^28+590x^29+1005x^30+340x^31+646x^32+226x^33+115x^34+24x^35+23x^36+4x^37

The gray image is a code over GF(2) with n=240, k=12 and d=108.
This code was found by Heurico 1.16 in 0.062 seconds.