The generator matrix

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

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+408x^80+716x^82+942x^84+556x^86+537x^88+316x^90+292x^92+164x^94+99x^96+40x^98+12x^100+11x^104+2x^108

The gray image is a code over GF(2) with n=344, k=12 and d=160.
This code was found by Heurico 1.16 in 4.3 seconds.