The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+50x^81+33x^82+126x^83+295x^84+62x^85+274x^86+88x^87+19x^88+46x^89+11x^90+8x^91+5x^92+2x^93+1x^94+2x^99+1x^134

The gray image is a code over GF(2) with n=680, k=10 and d=324.
This code was found by Heurico 1.16 in 0.703 seconds.