The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+88x^26+738x^27+990x^28+1586x^29+1668x^30+1420x^31+777x^32+660x^33+164x^34+66x^35+22x^36+10x^37+2x^40

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 0.25 seconds.