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  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 2X+2  1
 0  2  0 2X+2  0  0 2X+2 2X+2 2X  2  0  2 2X  0 2X+2  2  0 2X+2  2  0 2X+2 2X 2X 2X+2 2X+2  0 2X+2  0 2X 2X  2 2X+2  0 2X 2X+2  2  0 2X  2  2 2X  0  0  2  2 2X  2  2  2  2 2X 2X+2  0 2X+2  0 2X 2X 2X+2  2  0 2X  0  2  2  2 2X+2 2X+2 2X+2 2X+2 2X+2  2  2 2X  0 2X  0  2  0  2  2  0  2
 0  0  2 2X+2  0  2 2X+2 2X 2X+2 2X  0 2X+2 2X+2  0  2  0 2X+2 2X+2 2X  0  0  0 2X+2  2  0 2X 2X+2  2 2X  2 2X+2 2X  0 2X+2 2X+2  0  2  0 2X 2X+2 2X 2X 2X+2  2  0  2 2X+2  0  2  0  2  2 2X+2 2X 2X 2X+2 2X 2X+2  2  0  0  2 2X 2X 2X+2 2X  0  2  0 2X  2 2X+2  2 2X+2  2 2X+2  0 2X  0 2X  0  0
 0  0  0 2X  0  0 2X  0 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0 2X  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0  0 2X
 0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X  0  0  0  0  0  0  0  0  0 2X  0  0 2X 2X 2X
 0  0  0  0  0 2X  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0 2X  0 2X 2X  0

generates a code of length 82 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+76x^76+70x^78+158x^80+128x^81+1198x^82+128x^83+144x^84+66x^86+64x^88+10x^90+4x^92+1x^160

The gray image is a code over GF(2) with n=656, k=11 and d=304.
This code was found by Heurico 1.16 in 0.735 seconds.