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

generates a code of length 97 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+145x^86+4x^87+361x^88+40x^89+512x^90+120x^91+618x^92+248x^93+678x^94+384x^95+917x^96+440x^97+837x^98+408x^99+579x^100+264x^101+555x^102+92x^103+344x^104+32x^105+246x^106+16x^107+168x^108+81x^110+70x^112+13x^114+11x^116+4x^118+1x^120+1x^126+1x^128+1x^144

The gray image is a code over GF(2) with n=388, k=13 and d=172.
This code was found by Heurico 1.16 in 12.1 seconds.