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

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

Homogenous weight enumerator: w(x)=1x^0+32x^85+14x^86+13x^88+2x^90+1x^92+1x^100

The gray image is a code over GF(2) with n=340, k=6 and d=170.
This code was found by Heurico 1.16 in 0.426 seconds.