The generator matrix

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

generates a code of length 90 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+146x^85+743x^86+1146x^87+1164x^88+976x^89+893x^90+768x^91+692x^92+450x^93+364x^94+266x^95+229x^96+140x^97+118x^98+60x^99+17x^100+16x^101+1x^106+1x^108+1x^118

The gray image is a code over GF(2) with n=720, k=13 and d=340.
This code was found by Heurico 1.16 in 1.44 seconds.