The generator matrix

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

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+160x^82+88x^83+296x^84+92x^85+288x^86+92x^87+247x^88+76x^89+160x^90+72x^91+141x^92+76x^93+128x^94+4x^95+65x^96+12x^97+28x^98+9x^100+2x^102+5x^104+2x^108+2x^110+1x^112+1x^120

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 0.812 seconds.