The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+136x^27+1122x^28+348x^29+1128x^30+280x^31+787x^32+96x^33+136x^34+32x^35+26x^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 0.063 seconds.