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

generates a code of length 89 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+7x^88+100x^89+6x^90+10x^93+1x^98+2x^101+1x^106

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 0.797 seconds.