The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  X  1  X  1  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  0  2  0  2  2  2  2  2  2  0  0  2  2  2  0  2  0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  0
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  0  0  0  0  0  2  2  0  2  2  0  0  0  2  0  0  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  0  2  2  2  0  0  0  2  2  2  0  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  0  2  2  2  2  0  2
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0  0  0  0  2  2  2  0  2  0  2  0  2  0  0  0  2  2  2  2  2  0  2  2  0  2  2  0  0  2  0  2  2  0  2  2
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  2  0  0  2  2  0  0  0  2  0  2  0  2  0  2  2  0  2  0  2  2  2  0  0  2  2  2  0  2  0  0  0

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+14x^85+19x^86+32x^87+148x^88+16x^89+8x^90+8x^92+4x^94+3x^96+2x^117+1x^118

The gray image is a code over GF(2) with n=352, k=8 and d=170.
This code was found by Heurico 1.16 in 4.4 seconds.