The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+139x^80+324x^81+431x^82+598x^83+598x^84+610x^85+702x^86+616x^87+670x^88+590x^89+540x^90+548x^91+411x^92+410x^93+264x^94+214x^95+186x^96+114x^97+88x^98+46x^99+37x^100+12x^101+12x^102+6x^103+6x^104+4x^105+11x^106+4x^107

The gray image is a code over GF(2) with n=352, k=13 and d=160.
This code was found by Heurico 1.16 in 5.47 seconds.