The generator matrix

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

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+518x^26+1000x^27+2200x^28+2840x^29+3410x^30+2888x^31+1999x^32+904x^33+498x^34+48x^35+56x^36+22x^38

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 270 seconds.