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

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+169x^76+112x^78+233x^80+1024x^81+256x^82+154x^84+16x^86+69x^88+13x^92+1x^152

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 1.24 seconds.