The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+116x^73+805x^74+874x^75+1192x^76+980x^77+1225x^78+648x^79+737x^80+468x^81+399x^82+266x^83+264x^84+76x^85+69x^86+20x^87+36x^88+8x^89+5x^90+2x^96+1x^98

The gray image is a code over GF(2) with n=624, k=13 and d=292.
This code was found by Heurico 1.16 in 1.05 seconds.