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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+67x^78+183x^80+24x^81+229x^82+92x^83+238x^84+148x^85+217x^86+136x^87+211x^88+80x^89+168x^90+28x^91+78x^92+4x^93+57x^94+39x^96+23x^98+11x^100+7x^102+6x^104+1x^140

The gray image is a code over GF(2) with n=344, k=11 and d=156.
This code was found by Heurico 1.16 in 0.863 seconds.