The generator matrix

 1  0  1  1 3X+2  1  1  1 2X+2  1  1 3X  1  0  1  1  X  1  1  1  1 2X  1  1  1  X  X  1  1  1
 0  1  1 3X+2  1 3X+1  3 2X+2  1  X X+3  1 2X+2  1 3X+1 3X+2  1  3 3X+1  2  1 2X+2 3X 2X+1 X+1 3X+2  2 2X+1  3 2X+2
 0  0  X  0 2X 2X+2  2 3X 3X  X X+2 3X+2 3X+2 3X+2  X X+2 3X  X 2X+2  2 2X+2  X  0 X+2  0  X  X 2X  2  2
 0  0  0 2X 2X  0 2X  0  0 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X  0  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+52x^26+374x^27+487x^28+854x^29+725x^30+788x^31+352x^32+296x^33+85x^34+46x^35+23x^36+10x^37+1x^38+1x^40+1x^42

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 0.094 seconds.