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

generates a code of length 82 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+36x^78+96x^80+762x^82+92x^84+32x^86+2x^88+2x^90+1x^160

The gray image is a code over GF(2) with n=656, k=10 and d=312.
This code was found by Heurico 1.16 in 0.625 seconds.