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

generates a code of length 94 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+54x^82+56x^83+140x^84+184x^85+241x^86+274x^87+344x^88+404x^89+447x^90+550x^91+617x^92+608x^93+596x^94+588x^95+528x^96+572x^97+426x^98+392x^99+253x^100+204x^101+186x^102+142x^103+110x^104+64x^105+62x^106+42x^107+35x^108+12x^109+20x^110+4x^111+17x^112+9x^114+3x^116+5x^118+1x^122+1x^130

The gray image is a code over GF(2) with n=376, k=13 and d=164.
This code was found by Heurico 1.16 in 9.84 seconds.