The generator matrix

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

generates a code of length 93 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+180x^85+251x^86+540x^87+499x^88+674x^89+623x^90+748x^91+645x^92+644x^93+433x^94+596x^95+393x^96+514x^97+327x^98+336x^99+218x^100+196x^101+102x^102+104x^103+54x^104+56x^105+22x^106+6x^107+9x^108+8x^109+2x^110+4x^111+2x^112+2x^115+3x^120

The gray image is a code over GF(2) with n=372, k=13 and d=170.
This code was found by Heurico 1.16 in 6.2 seconds.