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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+180x^83+674x^84+1100x^85+1049x^86+1272x^87+838x^88+792x^89+610x^90+488x^91+366x^92+288x^93+169x^94+176x^95+85x^96+40x^97+44x^98+12x^99+2x^100+4x^101+1x^104+1x^112

The gray image is a code over GF(2) with n=704, k=13 and d=332.
This code was found by Heurico 1.16 in 1.28 seconds.