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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+3x^72+64x^73+95x^74+200x^75+311x^76+184x^77+95x^78+56x^79+4x^80+8x^81+1x^84+1x^86+1x^130

The gray image is a code over GF(2) with n=608, k=10 and d=288.
This code was found by Heurico 1.16 in 0.453 seconds.