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

generates a code of length 90 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+72x^84+278x^85+274x^86+354x^87+391x^88+480x^89+499x^90+474x^91+353x^92+320x^93+226x^94+226x^95+70x^96+24x^97+19x^98+14x^99+8x^100+2x^101+6x^102+4x^103+1x^156

The gray image is a code over GF(2) with n=720, k=12 and d=336.
This code was found by Heurico 1.16 in 1.25 seconds.