The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+142x^77+400x^78+652x^79+828x^80+956x^81+1202x^82+1040x^83+1382x^84+1260x^85+1373x^86+992x^87+1273x^88+1014x^89+995x^90+764x^91+681x^92+470x^93+351x^94+272x^95+144x^96+84x^97+51x^98+20x^99+9x^100+8x^101+12x^102+4x^103+2x^104+2x^105

The gray image is a code over GF(2) with n=344, k=14 and d=154.
This code was found by Heurico 1.16 in 16.6 seconds.