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

generates a code of length 79 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+128x^73+114x^74+274x^75+265x^76+434x^77+553x^78+712x^79+527x^80+428x^81+228x^82+162x^83+54x^84+104x^85+20x^86+30x^87+10x^88+20x^89+12x^90+4x^91+6x^92+6x^93+2x^95+1x^100+1x^134

The gray image is a code over GF(2) with n=632, k=12 and d=292.
This code was found by Heurico 1.16 in 1.14 seconds.