The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+228x^27+908x^28+508x^29+1064x^30+352x^31+655x^32+224x^33+104x^34+28x^35+20x^36+4x^37

The gray image is a code over GF(2) with n=240, k=12 and d=108.
This code was found by Heurico 1.16 in 0.062 seconds.