The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  0  1  X  1  1  1  1  1  1  1  1  1  1  2  1 X^2+X  1  0  X  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1 X+3 X^2+2  1 X^2+1  1 X^2+X  2 X+1 X^2+X X+1 X^2  0  X X^2+3  1  1  X  1  1  1  1  3 X^2+3  2
 0  0 X^2  0  0  2  0  2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2  0  2  2 X^2 X^2+2  2  2 X^2  2  2 X^2  2 X^2+2  0 X^2+2  0
 0  0  0 X^2+2  2 X^2 X^2  0 X^2 X^2+2  2 X^2  0 X^2  0  2 X^2+2 X^2+2  2  0 X^2  2 X^2+2  2  0 X^2 X^2+2  0  0 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+80x^26+194x^27+803x^28+398x^29+1204x^30+372x^31+771x^32+172x^33+64x^34+10x^35+8x^36+6x^37+12x^38+1x^44

The gray image is a code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 0.093 seconds.