The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+216x^82+362x^84+370x^86+283x^88+313x^90+248x^92+154x^94+58x^96+20x^98+6x^100+12x^102+3x^106+1x^120+1x^128

The gray image is a code over GF(2) with n=352, k=11 and d=164.
This code was found by Heurico 1.16 in 1.29 seconds.