The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+143x^80+466x^81+611x^82+896x^83+929x^84+1206x^85+1078x^86+1360x^87+1133x^88+1224x^89+1251x^90+1180x^91+1036x^92+1040x^93+694x^94+682x^95+425x^96+406x^97+228x^98+146x^99+99x^100+48x^101+38x^102+38x^103+8x^104+4x^105+4x^106+2x^107+2x^108+6x^109

The gray image is a code over GF(2) with n=356, k=14 and d=160.
This code was found by Heurico 1.13 in 6.54 seconds.