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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+101x^80+257x^84+36x^86+365x^88+144x^90+128x^91+540x^92+640x^93+344x^94+1280x^95+648x^96+1280x^97+304x^98+640x^99+490x^100+128x^101+164x^102+315x^104+32x^106+186x^108+90x^112+57x^116+15x^120+6x^124+1x^152

The gray image is a code over GF(2) with n=384, k=13 and d=160.
This code was found by Heurico 1.16 in 12.9 seconds.