The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+196x^77+634x^78+822x^79+502x^80+454x^81+375x^82+300x^83+190x^84+242x^85+148x^86+90x^87+73x^88+40x^89+24x^90+1x^92+2x^94+1x^96+1x^102

The gray image is a code over GF(2) with n=648, k=12 and d=308.
This code was found by Heurico 1.16 in 0.406 seconds.