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  2  1  2  1  X  1  X  1  1
 0  X  0  0  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  X  0  X  0  2 X+2 X+2  2  2 X+2  2 X+2  2 X+2 X+2  2  2 X+2  2 X+2  2 X+2 X+2  2  2 X+2  2 X+2  2 X+2  X  2  2  2  0 X+2 X+2  X X+2  0  2  0  0  X  X  X X+2  X  0  X  X X+2  2  X  0  0
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  2  2 X+2 X+2 X+2 X+2  2  2  2 X+2  2 X+2 X+2 X+2  2  2 X+2 X+2  2  0  0  2 X+2 X+2  X  X  0  2 X+2  2  X  0  0  0 X+2  X  0 X+2  X  2  0  2  X X+2  X  X  2  2  0  0  X X+2  X  X  0  2  0  2  X  X  0  X  0  2  0
 0  0  0  X  X  0  X  X  2 X+2 X+2  2  2 X+2 X+2  2  2  X X+2  0  2  X X+2  0  0  0 X+2 X+2  X  2  X  2  X  0 X+2  X  0  0 X+2  0 X+2  2  2  X  2  2  X X+2  2 X+2  X  0  X X+2  2  2  0 X+2  X  2  0 X+2  X  0  0  X  X  0  0 X+2  X  2 X+2  0  2  X  0 X+2 X+2  X  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+18x^77+46x^78+62x^79+88x^80+96x^81+81x^82+64x^83+22x^84+14x^85+16x^86+2x^87+1x^88+1x^154

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 0.291 seconds.