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

generates a code of length 79 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+166x^75+102x^76+186x^77+293x^78+588x^79+283x^80+196x^81+62x^82+110x^83+22x^84+34x^85+4x^86+1x^150

The gray image is a code over GF(2) with n=632, k=11 and d=300.
This code was found by Heurico 1.16 in 0.594 seconds.