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

generates a code of length 79 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+100x^76+64x^77+224x^78+256x^79+234x^80+64x^81+48x^82+32x^84+1x^144

The gray image is a code over GF(2) with n=632, k=10 and d=304.
This code was found by Heurico 1.16 in 71.4 seconds.