The generator matrix

 1  0  0  1  1  1  0  1 X+2  X  1  X  1  1  1  X  2  1  1  2  1  1  X  1  0  1  1 X+2  1  1  2  1 X+2  1  1  0  X  0  1  1  1  1  0  1  X X+2  1 X+2  0  1  1  1  1  1  2 X+2  1  1  2  X  1  1  1  1  1 X+2  0  1  1  1  2  1  1  1  1  1  X  X  1 X+2  1  1 X+2  0  1  1
 0  1  0  0  1  1  1  X  1 X+2 X+2  1  3  3  X  1  X X+3 X+1  1  0  X  1  2 X+2  3 X+1  1 X+2 X+3  1  2  0 X+3 X+1  1  1  0  X  0 X+2  3  1  X  1  1  3  X  1 X+3  2  X  1 X+1  1  1  3  2  1  1  3 X+3 X+1 X+3 X+1  1  1 X+3  2  0  X  0  3 X+3 X+1  3  1  1  2  2 X+2 X+2  X  1  X  1
 0  0  1 X+1 X+3  0 X+1  3  2  1  0  1  1 X+2 X+3  X  1  2  1  1  3  X X+1  2  1  2  3  0  1 X+2  X X+2  1 X+1 X+1 X+1 X+3  1  0  0 X+3  X  3  3 X+2 X+3 X+1  1  0 X+3  1  1 X+1  X  0 X+1  X  3  0  0 X+2  2  3  2 X+2  2  2 X+2 X+1  3  1 X+3  X X+1 X+1  1 X+2 X+1  2  1 X+1  2  1 X+2  2  3
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  0  2  2  2  0  2  0  2  0  2  0  2  2  0  2  2  0  2  0  0  0  0  2  2  0  2
 0  0  0  0  2  0  2  2  0  2  2  0  0  2  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  2  0  0  0  2  0  2  2  2  0  2  2  0  0  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  2  2  2
 0  0  0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  0  2  2  2  0  0  2  0  2  0  2  2  0  2  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  0  2  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2  0  2  0  0  2  0  0  2  2  2  2  2  2  2  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+440x^80+688x^82+874x^84+608x^86+571x^88+320x^90+274x^92+144x^94+111x^96+32x^98+20x^100+13x^104

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 56.3 seconds.