The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+166x^27+162x^28+202x^29+112x^30+148x^31+63x^32+56x^33+30x^34+50x^35+14x^36+14x^37+4x^39+2x^42

The gray image is a code over GF(2) with n=120, k=10 and d=54.
This code was found by Heurico 1.16 in 17.7 seconds.