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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+32x^77+16x^78+126x^80+192x^81+96x^82+32x^85+16x^86+1x^160

The gray image is a code over GF(2) with n=324, k=9 and d=154.
This code was found by Heurico 1.16 in 7.01 seconds.