The generator matrix

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

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+60x^26+150x^27+288x^28+232x^29+586x^30+274x^31+282x^32+88x^33+56x^34+18x^35+4x^36+2x^38+6x^39+1x^48

The gray image is a code over GF(2) with n=240, k=11 and d=104.
This code was found by Heurico 1.16 in 0.047 seconds.