The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+327x^84+478x^86+389x^88+306x^90+185x^92+150x^94+97x^96+46x^98+44x^100+12x^102+12x^104+1x^112

The gray image is a code over GF(2) with n=356, k=11 and d=168.
This code was found by Heurico 1.16 in 1.02 seconds.