The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+54x^81+164x^82+238x^83+208x^84+236x^85+213x^86+166x^87+154x^88+104x^89+115x^90+104x^91+72x^92+32x^93+51x^94+30x^95+19x^96+26x^97+9x^98+22x^99+8x^100+12x^101+8x^102+2x^104

The gray image is a code over GF(2) with n=348, k=11 and d=162.
This code was found by Heurico 1.11 in 0.449 seconds.