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

generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+147x^80+96x^83+151x^84+1344x^85+96x^87+148x^88+64x^92+1x^164

The gray image is a code over GF(2) with n=680, k=11 and d=320.
This code was found by Heurico 1.16 in 7.34 seconds.