The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+200x^83+634x^84+1062x^85+1152x^86+1136x^87+934x^88+904x^89+528x^90+444x^91+356x^92+254x^93+263x^94+136x^95+81x^96+60x^97+16x^98+20x^99+8x^101+1x^104+1x^110+1x^112

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 1.34 seconds.