The generator matrix

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

generates a code of length 92 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+408x^86+836x^88+760x^90+656x^92+484x^94+377x^96+200x^98+179x^100+96x^102+50x^104+32x^106+12x^108+4x^110+1x^116

The gray image is a code over GF(2) with n=368, k=12 and d=172.
This code was found by Heurico 1.11 in 5.42 seconds.