The generator matrix

 1  0  1  1  1 X+2  1  1  0 X+2  1  1  1  1  X  1  2  1 X+2  1  1  1 X+2  0  1  1  1  1  X  1  1  2  X  1  1  1  1  1  X  1  X  1  1  1  X  2  0  1  1  1  1  1  2  2  1 X+2  1 X+2  1  1  1  1  1 X+2  1 X+2  1  1  1  1  2  1  1  X  2  1  0  1  1  1  1  1  1  1  X  1  1  1  X  1  2  1  1  X  X X+2  1  1
 0  1  1  0  1  1  X X+3  1  1 X+3  2  X X+1  1  X  1  1  1  3  0 X+3  1  1  0  X  1  0  1 X+1 X+1  1  1  2  0 X+3 X+2  1  1  X  1  3 X+1  3  1  1  1 X+1 X+2  X  3  0  1  1  X  1 X+1  1  X  3 X+2 X+1 X+1  1  2  1  1  0  X  0  1  3  3  1  1 X+1  1  0 X+1  2 X+3 X+1 X+3 X+3 X+2  0  X X+3  1  3  1 X+3  2 X+2  1  1  X X+3
 0  0  X  0  0  0  0  0  0  2 X+2  X X+2  2  0  X  X  X X+2  2 X+2  X X+2  X  X  X X+2  0  X  2  X  X X+2  X X+2  X  0 X+2  0  0  X  2  0  X X+2 X+2  0  0  2 X+2  2  X  0 X+2  0 X+2  X X+2 X+2 X+2  2  X  0  2  X  0  X  2  X  2  X X+2  2 X+2  2 X+2  0  X  0 X+2  X  X  X X+2  X  X  0  2 X+2  0  2  0  2  X  0  2  0  0
 0  0  0  X  0  0  X  2  X X+2  0 X+2  X  X  0  0  2  X X+2 X+2  2  X  0 X+2  X  2  X X+2  X  0  2 X+2  2  2  X  0  X X+2 X+2  2  2  2  0  2  X  0  2 X+2  2  X  2  2 X+2  0 X+2 X+2  X  2  X X+2 X+2  0 X+2  0  2 X+2 X+2  0  X  2  X  0 X+2  X  2  0  0  0  2  2  0  0  X X+2  0  0  2  0  X X+2  X  X  2  2  2  0  X  X
 0  0  0  0  X  0  0 X+2 X+2 X+2  2  X  X X+2  X X+2  0  0  0  X X+2  2  0  2  2  2  X  X  X  2  X X+2 X+2  0  0  X  X  X  2  X X+2  0  X X+2  0 X+2 X+2 X+2  0  2  2 X+2  X  0  2 X+2 X+2  0  2  X X+2  2  0  0  0  0 X+2  X  X X+2 X+2  2  2  2  X  2  X  0  0 X+2 X+2  X  X  2  0 X+2  2  X  X  X  2  0 X+2  X X+2 X+2  X  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  2  2  0  0  2  2  2  2  0  0  2  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  2  2  2  2  0  2  2  2  0  2  2  2  2  0  2  2  2  0  2  2  0
 0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  2  2  0  2  0  0  2  0  0  0  2  2  2  2  0  2  0  0  0  2  0  0  0  0  0  2  0  2  2  0  0  0  0  2  0  2  2  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  2  0  2  2  0  0  2  0

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+90x^87+194x^88+240x^89+436x^90+588x^91+676x^92+872x^93+1010x^94+1094x^95+1238x^96+1330x^97+1224x^98+1192x^99+1251x^100+1104x^101+919x^102+846x^103+622x^104+418x^105+343x^106+204x^107+126x^108+100x^109+68x^110+66x^111+33x^112+26x^113+27x^114+16x^115+18x^116+4x^117+3x^118+2x^121+1x^122+1x^130+1x^132

The gray image is a code over GF(2) with n=392, k=14 and d=174.
This code was found by Heurico 1.16 in 74.3 seconds.