The generator matrix

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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+174x^85+891x^86+1212x^87+1815x^88+1812x^89+2195x^90+1578x^91+1932x^92+1180x^93+1110x^94+750x^95+700x^96+380x^97+326x^98+142x^99+91x^100+46x^101+19x^102+14x^103+4x^104+8x^105+3x^106+1x^108

The gray image is a code over GF(2) with n=728, k=14 and d=340.
This code was found by Heurico 1.16 in 4.41 seconds.