The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+18x^29+84x^30+18x^31+2x^33+2x^34+2x^35+1x^36

The gray image is a code over GF(2) with n=240, k=7 and d=116.
This code was found by Heurico 1.16 in -3.24e-008 seconds.