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

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

Homogenous weight enumerator: w(x)=1x^0+32x^89+14x^90+6x^91+1x^92+5x^94+2x^95+2x^96+1x^98

The gray image is a code over GF(2) with n=712, k=6 and d=356.
This code was found by Heurico 1.16 in 0.5 seconds.