The generator matrix

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

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+115x^26+580x^27+1268x^28+1226x^29+2104x^30+1096x^31+1027x^32+468x^33+183x^34+68x^35+32x^36+18x^37+6x^38

The gray image is a code over GF(2) with n=240, k=13 and d=104.
This code was found by Heurico 1.16 in 0.266 seconds.