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

generates a code of length 87 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+56x^88+4x^90+2x^92+1x^96

The gray image is a code over GF(2) with n=696, k=6 and d=352.
This code was found by Heurico 1.16 in 0.532 seconds.