The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X X X X
0 2 0 2 0 2 0 2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2 2 2 2X+2 0 0 2X 2X 0 2X 0 2 2X+2 0
0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 0
0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 2X 0
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+30x^28+192x^30+31x^32+2x^44
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.