The generator matrix

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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+153x^84+804x^85+979x^86+1230x^87+831x^88+1192x^89+637x^90+780x^91+344x^92+444x^93+246x^94+262x^95+93x^96+60x^97+71x^98+24x^99+33x^100+4x^101+1x^102+1x^104+1x^106+1x^114

The gray image is a code over GF(2) with n=712, k=13 and d=336.
This code was found by Heurico 1.16 in 1.27 seconds.