The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  X  1  1  X  1  1  2  1  1  0  1  1 X+2  1  1  1  1  0 X+2  1  1  1  1  2  X  1  1  1  1  2  X  X  X  0  X  X  2  1  1  1  1  1  1  1  1  0 X+2  2  X  X  X  0  X  X  2  2  2  0  0  1  1  1  1  1  1  1  1  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  0 X+2 X+1  3  1  1  2  X X+3  1  1  1  2  X X+3  1  1  1  0 X+2  X  2  X  X  0 X+2 X+1  3  2  X X+3  1  1  1  1  1  0 X+2  X  2  X  X  0  2  2  0  0 X+1  2 X+3 X+2  X  3  1  0
 0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+11x^84+88x^85+11x^86+3x^88+8x^89+3x^90+1x^92+1x^94+1x^98

The gray image is a code over GF(2) with n=340, k=7 and d=168.
This code was found by Heurico 1.16 in 0.321 seconds.