The generator matrix

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

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+72x^27+49x^28+272x^29+288x^30+232x^31+42x^32+40x^33+16x^35+3x^36+8x^37+1x^56

The gray image is a code over GF(2) with n=240, k=10 and d=108.
This code was found by Heurico 1.16 in 0.078 seconds.