The generator matrix

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

generates a code of length 30 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+14x^29+103x^30+7x^32+2x^37+1x^46

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.