The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 1 1 1 1 1 1 X 1 1 X
0 2X 0 0 0 0 0 2X 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 2X
0 0 2X 0 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 2X 0 2X 2X 2X
0 0 0 2X 0 0 0 2X 0 2X 2X 0 0 2X 0 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 2X 2X 0 2X 2X 2X 2X
0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 0 2X 0 0 2X 0 0 2X 2X 2X
0 0 0 0 0 2X 0 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0
0 0 0 0 0 0 2X 2X 2X 0 2X 0 0 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 0 0 0 0 2X 0 0 2X
generates a code of length 33 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+40x^28+24x^30+85x^32+768x^33+32x^34+44x^36+8x^38+17x^40+4x^44+1x^56
The gray image is a code over GF(2) with n=264, k=10 and d=112.
This code was found by Heurico 1.16 in 0.031 seconds.