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 X^2 X^2  X  2
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2  0  2 X^2  0  2 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2+2  2  2  2  2  2  2 X^2+2  2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  0  0 X^2 X^2+2  2 X^2+2  0 X^2  0  2 X^2 X^2+2 X^2 X^2+2 X^2+2 X^2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2  2 X^2  2 X^2 X^2 X^2+2 X^2+2 X^2+2  2  2  2 X^2  2 X^2  2 X^2  2 X^2+2 X^2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  2 X^2+2  2  0  0  0 X^2  0 X^2+2  2 X^2+2 X^2+2
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  0  0
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  2  0  0  2  0  2  2  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2  2  0  0  2

generates a code of length 83 over Z4[X]/(X^3+2,2X) 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 89.4 seconds.