The generator matrix

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

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+158x^26+259x^28+256x^29+742x^30+256x^31+246x^32+90x^34+4x^36+34x^38+1x^44+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 95.4 seconds.