The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+110x^26+208x^27+538x^28+816x^29+786x^30+816x^31+503x^32+208x^33+86x^34+12x^36+6x^38+4x^42+2x^44

The gray image is a code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 0.109 seconds.