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

generates a code of length 89 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+68x^84+72x^85+82x^86+32x^87+488x^88+560x^89+500x^90+32x^91+72x^92+72x^93+58x^94+10x^96+1x^176

The gray image is a code over GF(2) with n=712, k=11 and d=336.
This code was found by Heurico 1.16 in 0.921 seconds.