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

generates a code of length 97 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+183x^88+56x^92+942x^96+512x^98+168x^100+119x^104+60x^112+6x^120+1x^176

The gray image is a code over GF(2) with n=388, k=11 and d=176.
This code was found by Heurico 1.16 in 68.7 seconds.