The generator matrix

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

generates a code of length 86 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+101x^82+248x^83+351x^84+266x^85+241x^86+216x^87+265x^88+180x^89+96x^90+48x^91+27x^92+2x^93+2x^96+2x^100+1x^118+1x^122

The gray image is a code over GF(2) with n=688, k=11 and d=328.
This code was found by Heurico 1.16 in 0.766 seconds.