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

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

Homogenous weight enumerator: w(x)=1x^0+36x^78+96x^80+250x^82+92x^84+32x^86+2x^88+2x^90+1x^160

The gray image is a code over GF(2) with n=328, k=9 and d=156.
This code was found by Heurico 1.16 in 0.403 seconds.