The generator matrix

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

generates a code of length 92 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+53x^80+86x^81+151x^82+246x^83+368x^84+534x^85+677x^86+808x^87+1034x^88+1112x^89+1268x^90+1358x^91+1265x^92+1346x^93+1178x^94+1114x^95+976x^96+784x^97+638x^98+440x^99+316x^100+180x^101+128x^102+98x^103+59x^104+42x^105+35x^106+28x^107+19x^108+12x^109+16x^110+4x^111+4x^112+3x^114+1x^118+1x^120+1x^122

The gray image is a code over GF(2) with n=368, k=14 and d=160.
This code was found by Heurico 1.16 in 23.2 seconds.