The generator matrix

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

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+546x^26+992x^27+2343x^28+2768x^29+3298x^30+2704x^31+2194x^32+880x^33+494x^34+80x^35+69x^36+14x^38+1x^40

The gray image is a code over GF(2) with n=240, k=14 and d=104.
This code was found by Heurico 1.16 in 17.6 seconds.