The generator matrix

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

generates a code of length 97 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+84x^90+258x^91+326x^92+434x^93+317x^94+448x^95+272x^96+376x^97+270x^98+262x^99+185x^100+184x^101+121x^102+120x^103+78x^104+108x^105+53x^106+52x^107+40x^108+30x^109+26x^110+28x^111+9x^112+4x^113+9x^114+1x^116

The gray image is a code over GF(2) with n=388, k=12 and d=180.
This code was found by Heurico 1.16 in 1.31 seconds.