The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1 3X  1  1  1  0  1  1 3X+2  2  1  1  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1 3X  1  1  0  1 3X+2  1  1  2  1  1  1  1 3X  1  1  0  1  1  0 3X+2 X+2  1  1 2X  1  1  1  1 X+2  1  1  1  2  1  1  1 2X  1  1 2X+2  1 3X+2  1  0  1 2X  1 3X  1  1  1 3X+2  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X  1 2X+1 X+1  0  1 3X+2 2X+3  1  1  2 X+3 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 2X+1  1 3X 3X+2  1 X+1  1  0 2X+3  1  2 X+3 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  1  1  0 X+1  1 X+2  3 3X+2 2X+3  1 3X+1 2X  2  1 X+3 X+3 2X  1 3X+3 2X+2  1 X+2  1  0  1 2X  1 3X  1  3 3X+2 2X+1  1 2X+3
 0  0 2X  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X  0  0  0  0
 0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X  0  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X  0  0 2X  0  0  0 2X  0
 0  0  0  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X  0 2X  0  0  0 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X 2X 2X 2X 2X  0 2X  0
 0  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X  0 2X  0  0 2X  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0  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+112x^83+614x^84+432x^85+64x^86+480x^87+695x^88+480x^89+64x^90+432x^91+600x^92+112x^93+7x^96+2x^116+1x^120

The gray image is a code over GF(2) with n=704, k=12 and d=332.
This code was found by Heurico 1.16 in 0.781 seconds.