The generator matrix

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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+178x^82+1010x^83+1537x^84+2458x^85+2784x^86+3430x^87+3298x^88+3898x^89+3636x^90+3374x^91+2191x^92+2106x^93+1134x^94+814x^95+415x^96+262x^97+128x^98+40x^99+31x^100+12x^101+10x^102+4x^103+14x^104+2x^106+1x^108

The gray image is a code over GF(2) with n=712, k=15 and d=328.
This code was found by Heurico 1.16 in 14.5 seconds.