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

generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+65x^76+32x^77+288x^78+256x^79+252x^80+448x^81+128x^82+256x^83+62x^84+32x^85+224x^86+2x^88+1x^92+1x^144

The gray image is a code over GF(2) with n=648, k=11 and d=304.
This code was found by Heurico 1.16 in 0.672 seconds.