The generator matrix

 1  0  1  1  1 X+2  1 2X+2  1  1  1 3X  1  1 2X  1 3X+2  1  1  1  2  1  1  X  1  1  0  1 X+2  1  1  0  1  1 X+2  1  1  X  1  1  2  1  1  2  1  1  X  1  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1 3X+2  0  1  1  1 3X  1  1 2X  1 2X  1  1  1  X  X  1  1 2X
 0  1 X+1 X+2  3  1 2X+1  1 2X+2 X+1 3X  1 3X+3 2X  1 3X+2  1 2X+3 X+3  2  1  X  1  1  0 X+1  1 X+2  1 3X+3 2X+3  1  0  X  1 3X+1  1  1  2 X+2  1 3X+3  2  1  3  X  1 2X+1  X  X  3 X+3  3 3X+3  1 3X+1  1 X+1 2X+3 X+3 X+1 2X+1 2X+3 2X+1 3X+1 3X+1 3X+1  1  1 2X 3X+2  1  1 2X+2  3 3X  1 3X+1 3X+1  2  1  1 3X+3 3X 3X+1 2X  1 X+3 2X+2  1
 0  0  2  0  0 2X  0 2X 2X 2X 2X  0 2X  2 2X+2 2X+2  2  2 2X+2  2 2X+2 2X+2 2X+2  2  0 2X  0  0  0 2X  2 2X+2  2  2 2X+2  2 2X+2  2 2X+2 2X+2  2 2X+2  0  0 2X  0  0 2X 2X+2 2X 2X+2 2X  0  2  2  2 2X 2X+2 2X 2X+2 2X  0 2X+2 2X+2 2X  0  0  2 2X+2  2  2 2X+2  0 2X 2X+2  0 2X  0  2  2  0 2X  0 2X 2X 2X+2  2 2X+2  2  2
 0  0  0 2X  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0  0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0  0  0  0  0 2X  0 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X 2X  0  0  0
 0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0  0 2X  0  0  0  0  0  0  0  0  0  0 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X 2X  0  0 2X  0  0  0 2X 2X  0 2X 2X 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+132x^85+328x^86+606x^87+328x^88+604x^89+455x^90+430x^91+232x^92+442x^93+254x^94+146x^95+22x^96+34x^97+31x^98+34x^99+8x^100+2x^101+1x^102+2x^105+2x^106+1x^126+1x^128

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 1.12 seconds.