The generator matrix

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

generates a code of length 94 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+56x^86+1108x^87+2246x^88+3130x^89+4409x^90+5498x^91+6182x^92+6894x^93+7399x^94+6874x^95+6085x^96+5360x^97+3989x^98+2604x^99+1447x^100+1090x^101+601x^102+274x^103+178x^104+54x^105+30x^106+10x^107+9x^108+4x^110+4x^112

The gray image is a code over GF(2) with n=752, k=16 and d=344.
This code was found by Heurico 1.16 in 59.7 seconds.