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 X 0 X X^2+2 1 1 X 2 1 1 X X^2 1 1 1 1 1 X X X X X 0 1 X X^2+2 1 1 X 2 1 X X^2 1 1 1 X X X X X^2 0 X^2 2 1 X 1 0 X X^2+2 X X 2 X^2 1 1 X^2 X^2 1 1 1 1 X X 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X X^2+X X X+2 X 0 X^2+X X^2+X+2 X X^2+2 X+2 X X 2 X^2+X+2 X^2 X 0 2 X^2+2 X^2+X X^2 0 X X^2+X X+2 X X^2+2 X+2 X^2+X+2 X 2 X X X^2 X^2+X+2 X 0 X^2+2 2 X^2 X^2+2 X^2 X^2 X^2 0 X^2+X 2 X X+2 X X^2+X+2 X X X X^2+2 X^2 0 2 0 2 X^2+2 X^2 X^2+X X^2+X+2 0
generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 88.
Homogenous weight enumerator: w(x)=1x^0+4x^88+94x^89+6x^90+12x^91+3x^92+6x^93+1x^98+1x^110
The gray image is a code over GF(2) with n=712, k=7 and d=352.
This code was found by Heurico 1.16 in 0.5 seconds.