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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+136x^78+170x^80+80x^82+64x^84+40x^86+20x^88+1x^128

The gray image is a code over GF(2) with n=324, k=9 and d=156.
This code was found by Heurico 1.16 in 5.14 seconds.