The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+152x^26+228x^27+306x^28+256x^29+316x^30+228x^31+208x^32+108x^33+106x^34+72x^35+52x^36+4x^37+8x^38+1x^40+2x^42

The gray image is a code over GF(2) with n=120, k=11 and d=52.
This code was found by Heurico 1.16 in 0.0881 seconds.