The generator matrix

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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+286x^69+1576x^70+2876x^71+4231x^72+5976x^73+6337x^74+7800x^75+7589x^76+8156x^77+6765x^78+5392x^79+3780x^80+2392x^81+1252x^82+672x^83+247x^84+78x^85+77x^86+28x^87+12x^88+8x^89+1x^90+4x^92

The gray image is a code over GF(2) with n=608, k=16 and d=276.
This code was found by Heurico 1.16 in 45.1 seconds.