The generator matrix

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

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+36x^29+68x^30+8x^31+7x^32+4x^34+4x^37

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 0.016 seconds.