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

generates a code of length 91 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+72x^85+243x^86+272x^87+432x^88+408x^89+471x^90+452x^91+432x^92+420x^93+329x^94+184x^95+192x^96+84x^97+47x^98+16x^99+10x^100+8x^101+12x^102+4x^103+5x^104+1x^110+1x^150

The gray image is a code over GF(2) with n=728, k=12 and d=340.
This code was found by Heurico 1.16 in 1.28 seconds.