The generator matrix

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

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+101x^80+266x^81+555x^82+502x^83+731x^84+600x^85+769x^86+564x^87+700x^88+496x^89+573x^90+442x^91+423x^92+312x^93+383x^94+228x^95+173x^96+102x^97+138x^98+54x^99+42x^100+16x^101+12x^102+5x^104+2x^106+2x^107

The gray image is a code over GF(2) with n=352, k=13 and d=160.
This code was found by Heurico 1.13 in 1.94 seconds.