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

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

Homogenous weight enumerator: w(x)=1x^0+20x^77+99x^78+138x^79+163x^80+234x^81+157x^82+76x^83+64x^84+32x^85+23x^86+10x^87+4x^88+2x^89+1x^130

The gray image is a code over GF(2) with n=648, k=10 and d=308.
This code was found by Heurico 1.16 in 0.437 seconds.