The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+250x^28+224x^29+240x^30+72x^31+111x^32+80x^33+32x^34+8x^35+4x^36+2x^44

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 1.06 seconds.