The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+386x^71+1674x^72+2752x^73+4380x^74+5480x^75+7292x^76+6808x^77+8593x^78+7244x^79+6716x^80+5212x^81+4165x^82+2158x^83+1518x^84+672x^85+271x^86+94x^87+49x^88+28x^89+23x^90+14x^91+4x^92+2x^96

The gray image is a code over GF(2) with n=624, k=16 and d=284.
This code was found by Heurico 1.16 in 51.4 seconds.