The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^29+80x^30+15x^32+4x^37

The gray image is a code over GF(2) with n=120, k=7 and d=58.
This code was found by Heurico 1.13 in 0.171 seconds.