The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2) 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.