The generator matrix

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

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+48x^28+58x^29+69x^30+28x^31+30x^32+10x^33+10x^34+1x^36+1x^50

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 0.00796 seconds.