The generator matrix

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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+202x^68+1572x^69+2940x^70+5398x^71+7084x^72+10752x^73+12967x^74+16696x^75+15808x^76+17150x^77+12889x^78+11072x^79+7077x^80+4822x^81+2352x^82+1302x^83+503x^84+302x^85+105x^86+38x^87+8x^88+10x^89+11x^90+6x^91+5x^92

The gray image is a code over GF(2) with n=608, k=17 and d=272.
This code was found by Heurico 1.16 in 173 seconds.