The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+71x^28+32x^29+48x^30+32x^31+70x^32+1x^44+1x^48

The gray image is a code over GF(2) with n=120, k=8 and d=56.
This code was found by Heurico 1.16 in 0.00817 seconds.