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 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 X 1 1 X 1 1 1 1 X 1 2 1 1 1 X 1 X 1 1 1 X 1 0 0 0 1 1 1
0 X 0 0 0 2 0 2 0 X X X+2 X X+2 X+2 X 2 X X+2 0 2 0 X X 2 X 0 2 X+2 X+2 X 0 X+2 0 X+2 X+2 0 X+2 2 2 X X+2 0 2 X+2 X+2 X+2 X+2 0 2 0 0 X X+2 2 2 0 0 2 X+2 X+2 2 0 X+2 X+2 0 0 0 X X X 0 X X X+2 0 2 2 0 0 X+2 2 2 2 2 X X+2 2 X+2
0 0 X 0 0 2 X X X X+2 X 2 X X+2 0 0 0 2 X X+2 X 0 X+2 2 X+2 X 2 X 0 2 X 2 X X+2 0 X+2 0 2 0 X 0 0 X+2 X X+2 2 X X 0 X 0 X X+2 2 2 2 X 2 0 2 2 X+2 X 2 0 2 X+2 2 X 2 2 X X+2 X 0 0 X+2 X+2 2 0 X+2 2 0 0 2 X+2 2 X+2 X
0 0 0 X 0 X X X+2 2 0 X X 0 X+2 X 2 X+2 X 2 X 2 0 X+2 2 X 2 X 0 X+2 0 X+2 0 X+2 0 0 2 2 X+2 X+2 0 0 X+2 X+2 X+2 X+2 2 2 0 2 X+2 X+2 X+2 X+2 0 X 2 2 X 2 X+2 0 X+2 X+2 2 0 X+2 X 2 2 X+2 X 0 0 X+2 X+2 0 X+2 X+2 X+2 X 0 0 2 X X 2 X 2 X
0 0 0 0 X X 2 X X+2 X X 0 0 2 X X 0 X+2 X+2 0 2 2 X X X+2 0 X+2 X 0 2 2 X+2 0 2 0 X+2 X+2 2 X X+2 X+2 X+2 X 2 X X+2 0 X 0 0 2 X 2 X+2 0 X X 0 X X+2 X 0 2 X X X 2 X+2 X 0 2 X+2 X+2 X 2 X+2 2 X+2 0 2 2 X+2 2 X+2 X X 2 2 X+2
generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.
Homogenous weight enumerator: w(x)=1x^0+168x^82+4x^83+105x^84+112x^85+232x^86+228x^87+61x^88+320x^89+144x^90+268x^91+33x^92+80x^93+118x^94+12x^95+33x^96+70x^98+13x^100+26x^102+8x^104+10x^106+1x^108+1x^152
The gray image is a code over GF(2) with n=356, k=11 and d=164.
This code was found by Heurico 1.16 in 42.4 seconds.