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 2X  1  1  1  1  1  1  1  0  X  1  1  1  2  X
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 3X 2X+2 2X 3X+2  2 3X  0 X+2 3X 2X+2 X+2  0 2X+2 3X  0 X+2 2X+2 3X 2X 3X+2  2  X  0 X+2 2X+2 3X 3X+2  0  X  2 X+2 2X  2 3X 3X+2 2X 2X+2  X  0 2X  0 2X X+2 X+2 3X+2 3X+2 2X+2 2X+2  2  2 3X 3X  X  X 2X  0  0 2X 2X X+2 X+2 3X+2  X X+2  0  0 2X+2 2X+2 X+2
 0  0 2X  0  0  0 2X  0  0  0  0 2X  0  0 2X  0  0 2X 2X  0 2X  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0  0  0 2X 2X  0  0  0  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0
 0  0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0  0 2X  0 2X 2X 2X
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0 2X  0 2X  0  0 2X  0  0 2X 2X 2X  0 2X 2X

generates a code of length 79 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+35x^74+96x^75+180x^76+336x^77+169x^78+416x^79+363x^80+192x^81+45x^82+64x^83+95x^84+48x^85+7x^86+1x^148

The gray image is a code over GF(2) with n=632, k=11 and d=296.
This code was found by Heurico 1.16 in 26.8 seconds.