The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  2  X  X  1  1  1  1  0  1  1 X+2  1  1  1  1  1  1  0  1  1  X  0  1  1 X+2  1  1  1  1  1  1  0 X+2  1  1  2 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  X  1  2  1  X  0  1  1  1  1  1  0  X  1  2  1  1 X+2
 0  1  1 X+2 X+1  1  3  2  1  X X+3  1  1  1  0  1 X+2  2  1 X+3  X  1  1 X+3 X+3  1 X+1  0  1  3  X  1  1  0 X+2  1 X+3  1 X+3  0  1 X+2  1  1  2 X+2  1  1 X+1  3 X+1  3 X+1 X+1  3  3 X+1  3 X+1  3  2  1  X  1  2  1  X  1  0 X+3  1  0 X+2  X  1  2  1  X X+3 X+2  1
 0  0  X  0  2  0  2  X  X  X  X X+2  0  X  0 X+2 X+2 X+2  0  2  0 X+2  2 X+2  X  X  0 X+2 X+2  0 X+2 X+2  X  X  X  X X+2 X+2  0  2  0  2  2  2  2  2  2  2 X+2 X+2  X  X  0 X+2 X+2  0  X  X  2  2  X  X  X  X X+2 X+2 X+2 X+2  X  2  2  X  0  2  X X+2  X X+2 X+2 X+2  0
 0  0  0  2  2  2  0  2  2  0  2  0  0  0  2  0  2  0  2  2  0  2  0  2  0  2  0  0  0  2  2  2  2  2  0  0  0  2  0  2  2  0  2  0  0  2  0  2  0  2  0  2  2  2  0  0  2  0  0  2  0  0  2  2  2  2  0  0  0  0  2  0  0  2  0  2  0  2  2  0  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+61x^78+52x^79+181x^80+44x^81+58x^82+12x^83+54x^84+20x^85+17x^86+8x^88+1x^92+1x^96+1x^108+1x^112

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 0.373 seconds.