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.