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

generates a code of length 99 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+71x^86+142x^87+244x^88+266x^89+367x^90+406x^91+498x^92+682x^93+689x^94+944x^95+1007x^96+1166x^97+1266x^98+1092x^99+1203x^100+1262x^101+1029x^102+844x^103+740x^104+546x^105+451x^106+356x^107+289x^108+218x^109+154x^110+148x^111+80x^112+70x^113+52x^114+32x^115+25x^116+14x^117+16x^118+2x^119+8x^120+2x^123+1x^124+1x^142

The gray image is a code over GF(2) with n=396, k=14 and d=172.
This code was found by Heurico 1.16 in 35.4 seconds.