The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+168x^74+176x^75+592x^76+472x^77+638x^78+384x^79+511x^80+208x^81+414x^82+272x^83+115x^84+24x^85+84x^86+23x^88+6x^90+4x^92+2x^94+1x^108+1x^112

The gray image is a code over GF(2) with n=632, k=12 and d=296.
This code was found by Heurico 1.16 in 0.813 seconds.