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

generates a code of length 83 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+135x^80+64x^81+216x^82+128x^83+358x^84+64x^85+8x^86+47x^88+2x^92+1x^152

The gray image is a code over GF(2) with n=664, k=10 and d=320.
This code was found by Heurico 1.16 in 88.8 seconds.