The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+226x^69+1288x^70+3086x^71+5924x^72+9710x^73+14762x^74+20790x^75+26681x^76+30966x^77+33923x^78+32266x^79+27334x^80+21226x^81+15061x^82+9020x^83+5083x^84+2622x^85+1247x^86+548x^87+217x^88+78x^89+53x^90+12x^91+8x^92+2x^93+2x^94+4x^95+2x^97+2x^99

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 767 seconds.