The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  0  X  0  1  1  2  1  1  X  X  1  1  1  2  1  1  0  1  1  1  X  1  0  X  1  1  1  2  X  1  X  1  X  2  1  0  X  0  1  1  1  2  X  1  1  0  1  X  1
 0  X  0  X  0  0  X X+2  0  2  X X+2  0  2  X  X X+2  0  X  0 X+2  2  0 X+2  X  0  X X+2  0 X+2  X  2  0  X  2  0 X+2 X+2  X  2  0  0  X  X X+2  X  X  2  X  X X+2  2  X  0  0 X+2  X  2 X+2  X  2  2  2  2 X+2  X X+2  2  0 X+2  X  X  2  X X+2  X  0  0  X  2  X  0  X  X  2  X  X  0  0  2 X+2  X
 0  0  X  X  0 X+2  X  0  0  X  X  2  2  X X+2  2  0  0  X  0 X+2  X X+2  2 X+2  X  2  0  2  X  X  0 X+2 X+2  2  0  2  0  X  X  X X+2 X+2  2  2  0  0  0  X  0  2  X  X X+2  2  X  X  X  2  0  X  X  0  X  X  X  0  2  0 X+2  X  0  2  0  X  X  X  0 X+2 X+2 X+2  X  2  0  X  0  X  X  X  2  2  X
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  2  2  2  0  2  0  2  0  2  0  2  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  2  0  2  2  2  2  0  0  0  0  0  2  0  0  0  0  0  2  2  0  0  2  2  2  0  0  0  2  0  2  2  0  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  0  0  2  2  0  0  0  2  0  2  2  0  0  2  2  0  0  2  0  0  0  2  0  0  0  2  0  2  2  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  0  0  2  2  0  2  2  2  0  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  2  0  2  0  2  2  2  0  0  2  0  0  2  2  2  2  0  2  2  2  0  2  0  0  2  2  2  0  0  0  0  0  0  0  0  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  2  0  0  2  2  0  0  2  0  0  2  0  2  2  2  2  0  2  2  0  0  0  0  2  2  0  2  0  0  2  0  2  2  2  0  0  2  0  2  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  2  0  2  0  2  2  2  2  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  2  0  0  0  2  2  0  2  0  2  0  0  0  2  2  2  2  0  2  0  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  2  2  2  0  2  2  0  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  2  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  0  0  0  2  0  0  2  2  2  0  0  2  2  2  2  0  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+68x^80+62x^81+100x^82+160x^83+199x^84+354x^85+206x^86+580x^87+206x^88+818x^89+193x^90+1130x^91+213x^92+1148x^93+190x^94+804x^95+154x^96+534x^97+176x^98+288x^99+99x^100+126x^101+105x^102+88x^103+56x^104+26x^105+33x^106+22x^107+23x^108+4x^109+14x^110+3x^112+2x^114+2x^116+4x^118+1x^134

The gray image is a code over GF(2) with n=368, k=13 and d=160.
This code was found by Heurico 1.16 in 9.91 seconds.