The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 X 1 X 1 1 1 1 1 X 1 X 1
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 2X 2X 2X 2X 2X 2X 0 2X
0 0 2X 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 0 2X 0 0 2X 0 0 0 0 0 2X
0 0 0 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 2X 2X 2X 0 0 0 0 2X 0 2X 2X 2X 0 2X 2X 2X 0 0 0 0
0 0 0 0 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 2X 0 2X 0 0 0 2X 2X 2X 0 0 2X 0 2X 2X 0 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 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 0 0 0 0 2X 2X 0 0 0 0 2X 2X
0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 2X 0 0 0
generates a code of length 35 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+24x^28+4x^29+53x^30+24x^31+34x^32+60x^33+30x^34+1616x^35+29x^36+60x^37+18x^38+24x^39+26x^40+4x^41+17x^42+10x^44+9x^46+3x^48+1x^52+1x^58
The gray image is a code over GF(2) with n=280, k=11 and d=112.
This code was found by Heurico 1.16 in 0.093 seconds.