The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+860x^82+1828x^83+3186x^84+4472x^85+5609x^86+6440x^87+7418x^88+6954x^89+7056x^90+6524x^91+5487x^92+3676x^93+2730x^94+1580x^95+926x^96+410x^97+175x^98+88x^99+51x^100+24x^101+33x^102+4x^103+3x^104+1x^114

The gray image is a code over GF(2) with n=712, k=16 and d=328.
This code was found by Heurico 1.16 in 48.5 seconds.