The generator matrix

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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+86x^71+725x^72+964x^73+1197x^74+1128x^75+977x^76+768x^77+685x^78+438x^79+574x^80+248x^81+202x^82+92x^83+38x^84+44x^85+11x^86+8x^87+4x^88+1x^90+1x^92

The gray image is a code over GF(2) with n=608, k=13 and d=284.
This code was found by Heurico 1.16 in 1 seconds.