The generator matrix

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

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+50x^80+64x^81+189x^82+282x^83+443x^84+392x^85+819x^86+572x^87+1258x^88+858x^89+1562x^90+956x^91+1684x^92+946x^93+1593x^94+798x^95+1229x^96+546x^97+750x^98+366x^99+375x^100+224x^101+143x^102+84x^103+63x^104+34x^105+34x^106+12x^107+6x^108+6x^109+19x^110+2x^111+6x^112+2x^113+9x^114+4x^116+2x^118+1x^120

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 24.2 seconds.