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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+66x^80+89x^82+16x^83+143x^84+112x^85+187x^86+112x^87+146x^88+16x^89+57x^90+56x^92+17x^94+3x^96+2x^98+1x^164

The gray image is a code over GF(2) with n=344, k=10 and d=160.
This code was found by Heurico 1.16 in 0.56 seconds.