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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+399x^84+88x^85+580x^86+224x^87+630x^88+384x^89+624x^90+256x^91+461x^92+72x^93+236x^94+60x^96+56x^98+15x^100+8x^102+1x^104+1x^148

The gray image is a code over GF(2) with n=712, k=12 and d=336.
This code was found by Heurico 1.16 in 3.83 seconds.