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

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+90x^84+224x^85+254x^86+408x^87+435x^88+520x^89+458x^90+522x^91+360x^92+240x^93+189x^94+144x^95+78x^96+84x^97+31x^98+30x^99+8x^100+4x^101+11x^102+4x^104+1x^146

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 1.24 seconds.