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

generates a code of length 98 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+96x^87+165x^88+194x^89+291x^90+156x^91+491x^92+234x^93+731x^94+230x^95+1049x^96+190x^97+951x^98+180x^99+874x^100+164x^101+682x^102+150x^103+434x^104+138x^105+207x^106+132x^107+121x^108+78x^109+53x^110+66x^111+54x^112+22x^113+23x^114+12x^115+10x^116+4x^117+6x^118+2x^119+1x^136

The gray image is a code over GF(2) with n=392, k=13 and d=174.
This code was found by Heurico 1.16 in 69.6 seconds.