The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1  0  1 X+2  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  X  1  2  X  2  X  2  2  X  2  1  X  2  2  X
 0  1 X+1 X+2  1  1 X+1  0  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  1  1  0 X+1  1 X+2 X+1  1  3  1  3  1  2  X X+3  3 X+3  1 X+3  3 X+3  1 X+3  1 X+3  3 X+3  1 X+3  1  1  1  1  2  1  1  1  1  1  1  1  1  X  1  2  2 X+2
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  0  2  0  0  2  2  0  0  2  0  2  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  2  0  2
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  2  0  2
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  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  0  2  2  0  2  0  2  0  0  2  0  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  2  0  0  0  0  2  0

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+105x^78+167x^80+138x^82+76x^84+13x^86+9x^88+1x^92+1x^100+1x^120

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 0.581 seconds.