The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+252x^83+146x^84+362x^85+103x^86+266x^87+82x^88+244x^89+86x^90+164x^91+23x^92+110x^93+27x^94+54x^95+21x^96+24x^97+5x^98+28x^99+14x^100+28x^101+2x^102+4x^103+1x^106+1x^108

The gray image is a code over GF(2) with n=352, k=11 and d=166.
This code was found by Heurico 1.16 in 7.2 seconds.