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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+45x^74+60x^75+150x^76+134x^77+220x^78+218x^79+327x^80+366x^81+509x^82+588x^83+582x^84+722x^85+587x^86+698x^87+545x^88+590x^89+417x^90+316x^91+268x^92+162x^93+184x^94+134x^95+128x^96+66x^97+61x^98+28x^99+36x^100+6x^101+15x^102+6x^103+7x^104+2x^105+7x^106+2x^108+2x^110+2x^116+1x^122

The gray image is a code over GF(2) with n=344, k=13 and d=148.
This code was found by Heurico 1.16 in 8.62 seconds.