The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+144x^83+166x^84+232x^85+102x^86+200x^87+165x^88+194x^89+91x^90+176x^91+105x^92+170x^93+84x^94+116x^95+32x^96+36x^97+1x^98+2x^99+4x^100+2x^101+6x^102+6x^104+6x^105+2x^106+2x^107+1x^114+1x^116+1x^122

The gray image is a code over GF(2) with n=356, k=11 and d=166.
This code was found by Heurico 1.16 in 10.2 seconds.