The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+551x^80+1136x^82+1492x^84+1348x^86+1122x^88+868x^90+758x^92+444x^94+284x^96+108x^98+70x^100+10x^104

The gray image is a code over GF(2) with n=348, k=13 and d=160.
This code was found by Heurico 1.13 in 262 seconds.