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

generates a code of length 82 over Z4[X]/(X^3+2,2X) 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 0.719 seconds.