The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+157x^74+612x^75+1094x^76+1100x^77+1057x^78+1020x^79+885x^80+626x^81+531x^82+434x^83+249x^84+154x^85+129x^86+62x^87+37x^88+24x^89+13x^90+5x^92+1x^96+1x^98

The gray image is a code over GF(2) with n=632, k=13 and d=296.
This code was found by Heurico 1.16 in 1.12 seconds.