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  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  X  1  X  1  0  X  1  0  1
 0  X  0  X  0  0  X  X  0  0  X  X  0  2  X X+2  2  2 X+2  X  2  0 X+2  X  2 X+2  0  X  0  2 X+2 X+2  0  X X+2  2  X  2  0 X+2  X  2  2  X  0  X X+2  0 X+2  0 X+2 X+2 X+2  0  2  0  X  X  2 X+2  2  2 X+2  0  X  2 X+2  2  X  X  2  2  X  X  2 X+2  2  0  0 X+2 X+2  X  0  0  0  X  X  0
 0  0  X  X  0 X+2  X  0 X+2  0  X  0 X+2  2 X+2  0  X  2  X  0  X  0  X  2  X  0  2 X+2  0 X+2  X  2  2  X  0  X  2  0  X X+2  0  2  X X+2  X X+2  2  2  0  0 X+2 X+2  2  2 X+2  X  X  0  2  2 X+2  0 X+2  X X+2  X  0  X  2  0  2  2  0 X+2 X+2  2  0 X+2  X  2 X+2 X+2 X+2  X X+2  2  2  0
 0  0  0  2  0  0  2  0  0  2  0  2  2  2  0  2  2  0  2  2  0  0  2  2  2  0  2  0  2  2  0  0  2  2  0  0  2  0  2  0  2  0  0  0  2  2  2  2  0  2  0  2  0  2  0  0  0  2  0  0  2  0  2  2  2  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0  0  2  0  2  0  2  0
 0  0  0  0  2  0  2  2  2  2  0  0  2  0  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  0  0  0  2  0  2  0  0  0  0  0  0  2  0  0  2  0  0  2  0  2  2  2  2  2  2  2  0  2  2  0  2  0  2  2  0  2  2  0  0  2  2  2  0  0  2  2  0  2  2  0  2  2  0
 0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  0  2  2  2  0  0  2  0  0  2  0  0  2  2  2  2  0  2  2  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  2  0  2  2  0  2  0  0  0  2  0  2  2  0  0  2  2  0  0  0  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+63x^82+99x^84+32x^85+146x^86+96x^87+191x^88+96x^89+119x^90+32x^91+69x^92+49x^94+20x^96+6x^98+3x^100+1x^102+1x^164

The gray image is a code over GF(2) with n=352, k=10 and d=164.
This code was found by Heurico 1.16 in 0.605 seconds.