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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+108x^82+178x^83+266x^84+216x^85+526x^86+462x^87+729x^88+440x^89+464x^90+202x^91+189x^92+120x^93+86x^94+34x^95+29x^96+8x^97+28x^98+4x^99+4x^102+1x^104+1x^156

The gray image is a code over GF(2) with n=704, k=12 and d=328.
This code was found by Heurico 1.16 in 1.17 seconds.