The generator matrix

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

generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+171x^82+430x^83+369x^84+562x^85+403x^86+362x^87+358x^88+566x^89+297x^90+314x^91+155x^92+54x^93+20x^94+14x^95+9x^96+2x^97+1x^100+2x^106+2x^110+2x^112+1x^116+1x^118

The gray image is a code over GF(2) with n=696, k=12 and d=328.
This code was found by Heurico 1.16 in 0.828 seconds.