The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+120x^75+710x^76+632x^77+722x^78+476x^79+475x^80+204x^81+268x^82+92x^83+110x^84+76x^85+122x^86+64x^87+21x^88+1x^92+1x^100+1x^104

The gray image is a code over GF(2) with n=632, k=12 and d=300.
This code was found by Heurico 1.16 in 0.359 seconds.