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

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

Homogenous weight enumerator: w(x)=1x^0+3x^76+54x^77+3x^78+2x^81+1x^82

The gray image is a code over GF(2) with n=608, k=6 and d=304.
This code was found by Heurico 1.16 in 0.265 seconds.