The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  1
 0 2X  0  0  0  0  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X  0
 0  0 2X  0  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X  0 2X  0  0
 0  0  0 2X  0  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0  0 2X  0
 0  0  0  0 2X  0  0 2X  0  0 2X 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0
 0  0  0  0  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0
 0  0  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0  0 2X 2X 2X 2X 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+20x^24+18x^26+24x^28+96x^29+784x^30+11x^32+32x^33+14x^34+8x^36+15x^38+1x^54

The gray image is a code over GF(2) with n=240, k=10 and d=96.
This code was found by Heurico 1.16 in 0.016 seconds.