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

generates a code of length 98 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+26x^89+92x^90+70x^91+61x^92+78x^93+132x^94+156x^95+139x^96+188x^97+208x^98+184x^99+149x^100+164x^101+119x^102+68x^103+16x^104+42x^105+64x^106+34x^107+11x^108+14x^109+16x^110+4x^112+4x^114+3x^116+4x^118+1x^166

The gray image is a code over GF(2) with n=392, k=11 and d=178.
This code was found by Heurico 1.16 in 27.2 seconds.