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

generates a code of length 87 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+652x^80+1750x^81+3226x^82+4618x^83+5606x^84+6582x^85+7390x^86+6952x^87+7714x^88+5924x^89+5123x^90+4030x^91+2742x^92+1640x^93+845x^94+390x^95+193x^96+94x^97+27x^98+8x^99+4x^100+10x^101+13x^102+2x^103

The gray image is a code over GF(2) with n=696, k=16 and d=320.
This code was found by Heurico 1.16 in 53.9 seconds.