The generator matrix

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

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+112x^83+53x^84+176x^85+62x^86+112x^87+57x^88+128x^89+41x^90+120x^91+15x^92+80x^93+11x^94+32x^95+2x^96+11x^98+8x^99+3x^118

The gray image is a code over GF(2) with n=352, k=10 and d=166.
This code was found by Heurico 1.16 in 50.6 seconds.