The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+348x^76+280x^77+450x^78+160x^79+286x^80+128x^81+240x^82+64x^83+51x^84+8x^85+22x^86+8x^90+1x^112+1x^116

The gray image is a code over GF(2) with n=632, k=11 and d=304.
This code was found by Heurico 1.16 in 0.406 seconds.