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.