The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X 2X+2  X  X  X 2X+2  X  0  X 2X  X  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X 2X 3X+2  2 3X 2X 3X+2  2  X X+2  X 3X  X  0 2X+2 X+2  X 3X  X 3X+2  X  0 2X+2
 0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0 2X 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+29x^28+72x^29+45x^30+80x^31+17x^32+8x^33+2x^34+1x^36+1x^38

The gray image is a code over GF(2) with n=240, k=8 and d=112.
This code was found by Heurico 1.16 in 0.015 seconds.