The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  X  X  1  1  X  X  X  X  X
 0 2X  0  0  0  0  0  0  0  0 2X 2X  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X  0
 0  0 2X  0  0  0  0  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0
 0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X 2X  0  0 2X  0
 0  0  0  0 2X  0  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X
 0  0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0  0  0 2X  0 2X  0 2X 2X  0 2X 2X
 0  0  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0 2X  0  0  0 2X  0
 0  0  0  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0  0 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 24.

Homogenous weight enumerator: w(x)=1x^0+80x^24+32x^26+129x^28+1600x^30+95x^32+32x^34+54x^36+24x^40+1x^44

The gray image is a code over GF(2) with n=240, k=11 and d=96.
This code was found by Heurico 1.16 in 0.063 seconds.