The generator matrix

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

generates a code of length 92 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+96x^82+230x^83+447x^84+588x^85+757x^86+960x^87+1043x^88+1126x^89+1202x^90+1278x^91+1278x^92+1248x^93+1218x^94+1114x^95+926x^96+858x^97+619x^98+418x^99+327x^100+224x^101+166x^102+84x^103+55x^104+46x^105+24x^106+10x^107+12x^108+4x^109+10x^110+2x^111+6x^112+2x^113+3x^114+1x^118+1x^128

The gray image is a code over GF(2) with n=368, k=14 and d=164.
This code was found by Heurico 1.16 in 20.5 seconds.