The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 2 1 1 1 X 1 1 2 1 1 0 1 X 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1
0 X 0 0 0 0 0 2 2 X X+2 X X X X+2 X 0 X+2 2 X 2 X 0 X 2 X+2 X 0 X+2 2 X+2 0 0 2 X+2 2 X+2 X X X X+2 X+2 0 X+2 X+2 X+2 2 X 0 X X 2 X 2 X 0 2 X+2 2 2 X 2 2 X+2 X 2 0 X 2 0
0 0 X 0 0 2 X+2 X X X X X X+2 0 0 0 2 2 X+2 X 2 0 0 X+2 2 2 X X+2 0 X X X+2 X X+2 0 X X+2 2 X 2 0 X X X 0 0 2 X+2 X+2 2 0 X+2 X 2 0 0 X 2 X 0 2 X+2 X X X 0 2 X 2 2
0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 0 X X 2 X 2 X+2 0 X+2 0 2 X 2 X X 2 X X 0 0 2 X X+2 0 0 2 2 0 X X X+2 X+2 0 0 X 2 0 X X X+2 X+2 2 2 2 0 X X 2 X+2 0 2 2 X+2 X 2 2 X+2 2
0 0 0 0 X X 2 X+2 X X+2 2 2 X 2 X+2 X X 2 2 X+2 0 X+2 0 X+2 X+2 X+2 0 X+2 0 X 0 2 0 X+2 X X+2 2 2 X X+2 2 X+2 X+2 0 0 X+2 X X X+2 X X X+2 0 0 0 2 2 2 0 X X 0 X+2 2 X+2 2 X+2 0 X+2 0
generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.
Homogenous weight enumerator: w(x)=1x^0+17x^62+74x^63+77x^64+102x^65+100x^66+180x^67+198x^68+200x^69+269x^70+166x^71+203x^72+136x^73+68x^74+64x^75+36x^76+58x^77+21x^78+20x^79+26x^80+14x^81+4x^82+8x^83+2x^84+2x^85+1x^86+1x^120
The gray image is a code over GF(2) with n=280, k=11 and d=124.
This code was found by Heurico 1.16 in 0.463 seconds.