The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^82+366x^83+283x^84+344x^85+232x^86+250x^87+179x^88+224x^89+30x^90+50x^91+13x^92+40x^93+6x^95+4x^100+2x^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 0.5 seconds.