The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+338x^28+368x^30+293x^32+16x^34+6x^36+2x^40

The gray image is a code over GF(2) with n=240, k=10 and d=112.
This code was found by Heurico 1.16 in 9.78 seconds.