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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+129x^82+16x^83+60x^84+144x^85+101x^86+208x^87+39x^88+112x^89+91x^90+32x^91+23x^92+55x^94+3x^96+8x^98+1x^100+1x^160

The gray image is a code over GF(2) with n=348, k=10 and d=164.
This code was found by Heurico 1.16 in 70.3 seconds.