The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+206x^69+1347x^70+2884x^71+5619x^72+10478x^73+14594x^74+20652x^75+26924x^76+31064x^77+33721x^78+31832x^79+27528x^80+21258x^81+14991x^82+9330x^83+4887x^84+2706x^85+1192x^86+536x^87+182x^88+108x^89+67x^90+14x^91+9x^92+4x^93+8x^94+2x^96

The gray image is a code over GF(2) with n=624, k=18 and d=276.
This code was found by Heurico 1.16 in 725 seconds.