The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+236x^70+1352x^71+3259x^72+5718x^73+9669x^74+15372x^75+20319x^76+27174x^77+30790x^78+33698x^79+31291x^80+28126x^81+20839x^82+14752x^83+9355x^84+5250x^85+2575x^86+1368x^87+593x^88+260x^89+74x^90+30x^91+10x^92+16x^93+8x^94+2x^95+2x^96+2x^99+2x^100+1x^102

The gray image is a code over GF(2) with n=632, k=18 and d=280.
This code was found by Heurico 1.16 in 766 seconds.