The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+656x^80+1684x^81+3292x^82+4752x^83+5720x^84+6302x^85+7408x^86+6570x^87+7668x^88+6466x^89+5381x^90+3820x^91+2662x^92+1474x^93+898x^94+434x^95+155x^96+90x^97+65x^98+24x^99+10x^100+4x^102

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 50.6 seconds.