The generator matrix

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

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+170x^75+652x^76+694x^77+672x^78+424x^79+428x^80+248x^81+213x^82+198x^83+168x^84+106x^85+89x^86+8x^87+13x^88+8x^89+2x^92+1x^94+1x^98

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 0.375 seconds.