The generator matrix

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

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+164x^85+263x^86+572x^87+531x^88+376x^89+460x^90+482x^91+352x^92+350x^93+248x^94+182x^95+54x^96+30x^97+4x^98+6x^99+1x^100+4x^101+4x^103+2x^105+2x^108+2x^109+2x^111+2x^112+1x^118+1x^124

The gray image is a code over GF(2) with n=720, k=12 and d=340.
This code was found by Heurico 1.16 in 0.921 seconds.