The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+224x^83+723x^84+882x^85+1305x^86+1026x^87+965x^88+760x^89+577x^90+432x^91+488x^92+290x^93+244x^94+106x^95+72x^96+44x^97+32x^98+8x^99+6x^100+1x^102+4x^103+1x^106+1x^108

The gray image is a code over GF(2) with n=704, k=13 and d=332.
This code was found by Heurico 1.16 in 1.42 seconds.