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  X  X  1  1  1  1  X  X  X  1  1  1  X  X  X  1  1  1  X  X  X X^2 X^2 X^2  X  1  1  X  X  X  X X^2 X^2 X^2  1  X  1  2  2  2  1  0  0  0  X X^2  1 X^2 X^2 X^2  X X^2  X  X  1  1
 0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  0  2  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  2  0  0  0  2  0  2  2  0  0  0  2  0  0
 0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  2  2  0  0  0  2  2  0  0  0  2  2  0  0

generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+32x^85+16x^86+5x^88+8x^90+2x^92

The gray image is a code over GF(2) with n=680, k=6 and d=340.
This code was found by Heurico 1.16 in 0.406 seconds.