The generator matrix

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

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+138x^69+678x^70+1608x^71+2145x^72+3036x^73+3199x^74+3794x^75+4123x^76+4074x^77+2942x^78+2668x^79+1745x^80+1164x^81+650x^82+446x^83+159x^84+84x^85+80x^86+12x^87+11x^88+11x^90

The gray image is a code over GF(2) with n=608, k=15 and d=276.
This code was found by Heurico 1.16 in 11.9 seconds.