The generator matrix

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

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+166x^82+768x^83+1204x^84+2036x^85+1672x^86+2338x^87+1595x^88+1652x^89+1179x^90+1266x^91+869x^92+768x^93+297x^94+290x^95+148x^96+68x^97+16x^98+22x^99+15x^100+4x^101+4x^102+4x^103+1x^110+1x^114

The gray image is a code over GF(2) with n=704, k=14 and d=328.
This code was found by Heurico 1.16 in 4.17 seconds.