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+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.